Gr 12 Mathematics: November Medium P(2)
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Questions and Answers

If the gradient of the radius of a circle is (\frac{1}{2}), what is the gradient of the tangent at the point of tangency?

  • -\(\frac{1}{2}\)
  • 2
  • -2 (correct)
  • \(\frac{1}{2}\)

In a circle with center (3, 4) and radius 5, what is the gradient of the radius drawn to the point (7, 1)?

  • -\(\frac{4}{3}\)
  • \(\frac{3}{4}\)
  • \(\frac{4}{3}\)
  • -\(\frac{3}{4}\) (correct)

A line parallel to one side of a triangle divides the other two sides proportionally. This theorem is known as:

  • Midpoint Theorem
  • Pythagorean Theorem
  • Angle Bisector Theorem
  • Basic Proportionality Theorem (correct)

In a triangle ABC, a line DE is drawn parallel to BC, dividing AB in the ratio 2:3. If AD = 8 cm, what is the length of DB?

<p>12 cm (A)</p> Signup and view all the answers

What is the area of a triangle with a base of 10 cm and a height of 6 cm?

<p>30 cm (C)</p> Signup and view all the answers

Given the equation of a circle: (x - 2) + (y + 1) = 9, what is the center of the circle?

<p>(2, -1) (C)</p> Signup and view all the answers

A ratio compares two quantities with the same units. Which of the following is NOT a ratio?

<p>10% (B)</p> Signup and view all the answers

If the equation of a tangent to a circle is y = 3x - 2, and the point of tangency is (1, 1), what is the gradient of the radius drawn to that point?

<p>-(\frac{1}{3}) (D)</p> Signup and view all the answers

Which of these properties is NOT a property of proportions?

<p>Direct Proportion (B)</p> Signup and view all the answers

Given a triangle ABC, a line DE is drawn parallel to BC, dividing AB in the ratio 2:1. If AD = 6 cm, what is the length of AB?

<p>12 cm (C)</p> Signup and view all the answers

What is the condition for two triangles to be similar?

<p>They have proportional sides and equal corresponding angles (B)</p> Signup and view all the answers

What is the formula for the area of a triangle?

<p>Area = 1/2 × base × height (B)</p> Signup and view all the answers

What is the Pythagorean theorem used for?

<p>To find the sum of squares of two sides of a right-angled triangle (B)</p> Signup and view all the answers

What is the regression coefficient r used for?

<p>To measure the strength of correlation between two sets of data (D)</p> Signup and view all the answers

What is the linear regression line used for?

<p>To find the equation of the line of best fit (A)</p> Signup and view all the answers

What is the converse of the Pythagorean theorem used for?

<p>To prove that an angle is a right angle (D)</p> Signup and view all the answers

What is the condition for two triangles to have areas proportional to their bases?

<p>They have equal heights (B)</p> Signup and view all the answers

What is the advantage of using the linear regression line?

<p>It helps in finding the pattern in a set of data (C)</p> Signup and view all the answers

What is the value of the regression coefficient r?

<p>Always between -1 and +1 (D)</p> Signup and view all the answers

What is the purpose of the Pythagorean theorem proof?

<p>To prove that the square on the hypotenuse is equal to the sum of the squares on the other two sides (A)</p> Signup and view all the answers

What is the formula for the area of a triangle?

<p>$rac{1}{2} \times \text{base} \times \text{height}$ (C)</p> Signup and view all the answers

What is the condition for two polygons to be similar?

<p>All pairs of corresponding angles are equal and all pairs of corresponding sides are in the same proportion. (C)</p> Signup and view all the answers

What is the statement of the Mid-point Theorem?

<p>The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length. (B)</p> Signup and view all the answers

What is the converse of the Mid-point Theorem?

<p>The line drawn from the midpoint of one side of a triangle bisects the third side of the triangle. (C)</p> Signup and view all the answers

What is the Proportion Theorem?

<p>If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. (C)</p> Signup and view all the answers

If two triangles are equiangular, what can be concluded about their corresponding sides?

<p>The corresponding sides are in the same proportion. (B)</p> Signup and view all the answers

What is the definition of similar polygons?

<p>Polygons that have the same shape but differ in size. (A)</p> Signup and view all the answers

To prove two triangles are similar, what condition must be shown?

<p>All pairs of corresponding angles are equal or all pairs of corresponding sides are in the same proportion. (C)</p> Signup and view all the answers

What does a correlation value of 0 indicate?

<p>No correlation (A)</p> Signup and view all the answers

What is the statement of the theorem: Triangles with Sides in Proportion are Similar?

<p>If the corresponding sides of two triangles are in proportion, then the two triangles are similar. (D)</p> Signup and view all the answers

What is the condition for two triangles to be equiangular?

<p>All pairs of corresponding angles are equal. (D)</p> Signup and view all the answers

What is the formula to calculate the linear correlation coefficient r?

<p>r = b * (σx / σy) (D)</p> Signup and view all the answers

What is the equation of a circle with center at the origin and radius r?

<p>x^2 + y^2 = r^2 (C)</p> Signup and view all the answers

What is the cosine of a difference formula in trigonometry?

<p>cos(α - β) = cos α cos β - sin α sin β (B)</p> Signup and view all the answers

What does a correlation value of -1 indicate?

<p>A perfect negative correlation (C)</p> Signup and view all the answers

What is the interpretation of a strong negative correlation?

<p>As x increases, y decreases (A)</p> Signup and view all the answers

What is the formula to calculate the gradient of the least squares regression line?

<p>B = r * (σy / σx) (B)</p> Signup and view all the answers

What is the equation of the regression line?

<p>y = A + Bx (D)</p> Signup and view all the answers

What is the sine of a sum formula in trigonometry?

<p>sin(α + β) = sin α cos β + cos α sin β (B)</p> Signup and view all the answers

What is the interpretation of a very strong correlation?

<p>0.9 &lt; r &lt; 1 (A)</p> Signup and view all the answers

What is the formula for the area of a trapezium (trapezoid)?

<p>$rac{1}{2} imes (base_1 + base_2) imes height$ (C)</p> Signup and view all the answers

Which statement accurately describes a property of similar triangles?

<p>Their corresponding angles are equal. (A)</p> Signup and view all the answers

How do you calculate the area of a rhombus using its diagonals?

<p>$rac{1}{2} imes diagonal_{AC} imes diagonal_{BD}$ (C)</p> Signup and view all the answers

In the context of triangle proportionality, if a line is drawn parallel to one side of a triangle, what happens to the other sides?

<p>They are divided in the same proportion. (B)</p> Signup and view all the answers

What is the area of a square if the length of one side is 5 units?

<p>25 square units (D)</p> Signup and view all the answers

Which theorem states that a line joining the midpoints of two sides of a triangle is parallel to the third side?

<p>Mid-point Theorem (D)</p> Signup and view all the answers

Which equation represents Pythagoras' Theorem in a right-angled triangle?

<p>$a^2 + b^2 = c^2$ (B)</p> Signup and view all the answers

If a triangle has a base of 8 units and a height of 5 units, what is its area?

<p>20 square units (B)</p> Signup and view all the answers

What is true regarding polygons that are similar?

<p>Their areas are proportional to the square of the ratio of their corresponding sides. (B)</p> Signup and view all the answers

What is the formula for the area of a rectangle?

<p>$length imes width$ (B)</p> Signup and view all the answers

What is the standard form of the equation for a circle with center at (3, -2) and radius 5?

<p>(x - 3)^2 + (y + 2)^2 = 25 (C)</p> Signup and view all the answers

What does the term 'perpendicularity' refer to in the context of a tangent to a circle?

<p>The radius at the point of tangency is perpendicular to the tangent line. (D)</p> Signup and view all the answers

Which step is NOT part of completing the square for the equation of a circle?

<p>Square both sides of the radius equation. (B)</p> Signup and view all the answers

If a circle's equation is given as (x + 2)^2 + (y - 5)^2 = 36, what is the radius of the circle?

<p>6 (D)</p> Signup and view all the answers

In the standard form of a circle's equation, what do the variables a and b represent?

<p>The center coordinates (x, y) of the circle. (D)</p> Signup and view all the answers

What is the first step in rearranging the general form of a circle's equation into standard form?

<p>Group the x terms and y terms. (A)</p> Signup and view all the answers

For a circle represented by the equation (x - 1)^2 + (y + 4)^2 = 16, what are the coordinates of the center?

<p>(1, -4) (B)</p> Signup and view all the answers

What is the relationship between the radius of a circle and the coordinates of a point on its circumference?

<p>The radius squared equals the sum of the differences squared. (D)</p> Signup and view all the answers

What is the compound angle formula for sin(α - β)?

<p>sin α cos β - cos α sin β (C)</p> Signup and view all the answers

What is the double angle formula for sin(2α)?

<p>2sin α cos α (D)</p> Signup and view all the answers

What is the general method for solving trigonometric equations?

<p>Simplifying, using reference angles, and adding multiples of the period (B)</p> Signup and view all the answers

What is the compound angle formula for cos(α + β)?

<p>cos α cos β - sin α sin β (D)</p> Signup and view all the answers

What is the double angle formula for cos(2α)?

<p>cos²α - sin²α (A), 2cos²α - 1 (B), 1 - 2sin²α (D)</p> Signup and view all the answers

What is the purpose of the CAST diagram?

<p>To determine where the function is positive or negative (B)</p> Signup and view all the answers

What is the co-function identity for cos(90° - α)?

<p>sin α (C)</p> Signup and view all the answers

What is the step in the general method for solving trigonometric equations that involves adding multiples of the period?

<p>Finding restricted values (A)</p> Signup and view all the answers

What is the compound angle formula for sin(α + β)?

<p>sin α cos β + cos α sin β (A)</p> Signup and view all the answers

What is the purpose of the reference angle in the general method for solving trigonometric equations?

<p>To determine the restricted values (A)</p> Signup and view all the answers

What is the formula used to calculate the area of triangle ABC if two sides and an included angle are known?

<p>Area = $rac{1}{2}bc imes an A$ (B)</p> Signup and view all the answers

Which rule should be used if two sides and the included angle of a triangle are known?

<p>Cosine Rule (C)</p> Signup and view all the answers

Under what condition would you use the Sine Rule?

<p>When two angles and a side are known (A)</p> Signup and view all the answers

What is the correct expression to find $ heta$ if $ an heta = x$?

<p>$ heta = an^{-1} x + k imes 180^ heta$ (A)</p> Signup and view all the answers

In triangle ABC, which ratio represents the Cosine Rule?

<p>$a^2 = b^2 + c^2 - 2bc imes an A$ (A)</p> Signup and view all the answers

What is the formula to calculate the height of a pole given distance AB and angle FBA?

<p>$h = rac{d imes an heta}{ an eta}$ (B)</p> Signup and view all the answers

When using the Cosine Rule, which variables are essential?

<p>Two sides and one angle (A)</p> Signup and view all the answers

To find the height of a building using the Sine Rule, which angles must be known?

<p>Both angles DBC and DCB (A)</p> Signup and view all the answers

What is the relationship between the distance formula and the cosine rule for points on the unit circle?

<p>Both express the distance between two points as a function of the cosine of their angle difference. (A)</p> Signup and view all the answers

Using the cosine rule, how is $KL^2$ expressed in relation to angles $eta$ and $eta$?

<p>$KL^2 = 2 - 2 ext{cos}(eta - eta)$ (B)</p> Signup and view all the answers

What simplification leads to the final expression for $ ext{cos}( heta)$ in terms of $ ext{cos}(eta)$ and $ ext{sin}(eta)$?

<p>The angle difference formula results in $ ext{cos}( heta) = ext{cos}(eta) ext{cos}(eta) + ext{sin}(eta) ext{sin}(eta)$ (A)</p> Signup and view all the answers

How is $ ext{cos}(eta)$ used in relation to the negative angle identity when deriving $ ext{cos}( heta)$?

<p>It is equal to $ ext{cos}(eta)$ regardless of the angle's sign due to even-odd identities. (B)</p> Signup and view all the answers

What simplification is made when deriving $ ext{cos}( heta)$ from the cosine difference formula?

<p>The addition is simplified to fit the angle addition theorem. (A)</p> Signup and view all the answers

What does the expression $ ext{cos}( heta) = ext{cos}(eta) ext{cos}(eta) - ext{sin}(eta) ext{sin}(eta)$ represent?

<p>It represents the cosine of the sum of two angles. (D)</p> Signup and view all the answers

What is the formula for the area of a kite?

<p>1/2 × diagonal AC × diagonal BD (D)</p> Signup and view all the answers

What is the condition for two polygons to be similar?

<p>The corresponding angles are equal, and the corresponding sides are in proportion (A)</p> Signup and view all the answers

What is the formula for the area of a parallelogram?

<p>base × height (B)</p> Signup and view all the answers

What is the statement of the Triangle Proportionality Theorem?

<p>If two triangles are equiangular, then the corresponding sides are in proportion (A)</p> Signup and view all the answers

What is the formula for the area of a trapezium?

<p>1/2 × (base1 + base2) × height (A)</p> Signup and view all the answers

If two triangles have equal heights, what can be concluded about their areas?

<p>They are proportional to their bases (C)</p> Signup and view all the answers

What is the statement of the Basic Proportionality Theorem?

<p>If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally (A)</p> Signup and view all the answers

What is the formula for the area of a rhombus?

<p>1/2 × diagonal AC × diagonal BD (D)</p> Signup and view all the answers

What is the condition for two triangles to have areas proportional to their bases?

<p>They have equal heights (D)</p> Signup and view all the answers

What is the formula for the area of a rectangle?

<p>length × width (A)</p> Signup and view all the answers

What is the equation of a circle with center at ( (2, -3) ) and radius ( 5 )?

<p>( (x - 2)^2 + (y + 3)^2 = 25 ) (D)</p> Signup and view all the answers

What is the center and radius of the circle represented by the equation ( x^2 + y^2 - 6x + 4y - 12 = 0 )?

<p>Center ( (3, -2) ), radius ( \sqrt{37} ) (C)</p> Signup and view all the answers

Given a circle with equation ( (x - 4)^2 + (y + 1)^2 = 9 ), what is the equation of the tangent line at the point ( (7, -1) )?

<p>( y = -rac{4}{3}x + rac{25}{3} ) (C)</p> Signup and view all the answers

Which of the following statements is true about the tangent line to a circle?

<p>The tangent line is perpendicular to the radius drawn to the point of tangency. (B)</p> Signup and view all the answers

What is the equation of the tangent to the circle ( x^2 + y^2 = 25 ) at the point ( (3, 4) )?

<p>( 3x + 4y = 25 ) (D)</p> Signup and view all the answers

What is the distance between the center of the circle ( (x - 3)^2 + (y + 2)^2 = 16 ) and the point ( (7, 1) )?

<p>( \sqrt{65} ) (A)</p> Signup and view all the answers

What is the equation of the circle with center ( (-1, 2) ) that passes through the point ( (3, 4) )?

<p>( (x + 1)^2 + (y - 2)^2 = 20 ) (B)</p> Signup and view all the answers

If a circle has a diameter of 10 units, what is its radius?

<p>( 5 ) (A)</p> Signup and view all the answers

What does the relationship between the gradients of the radius and the tangent in a circle indicate?

<p>Their product is -1. (D)</p> Signup and view all the answers

In order to find the gradient of the tangent at a point on a circle, what must be calculated first?

<p>The gradient of the radius. (B)</p> Signup and view all the answers

Which statement correctly defines a proportion?

<p>A statement that two ratios are equal. (A)</p> Signup and view all the answers

What is the condition for two triangles to be similar?

<p>They have corresponding sides in proportion (A)</p> Signup and view all the answers

What property of proportions states that if two ratios are equal, the cross-products are also equal?

<p>Cross multiplication. (C)</p> Signup and view all the answers

In which form can a ratio be expressed?

<p>As a fraction. (D)</p> Signup and view all the answers

What is the purpose of the Pythagorean theorem?

<p>To find the length of the hypotenuse of a right-angled triangle (B)</p> Signup and view all the answers

If a line is drawn parallel to one side of a triangle, which effect does it have on the other sides?

<p>It divides the other sides proportionally. (B)</p> Signup and view all the answers

What is the equation of a linear regression line?

<p>y = A + Bx (C)</p> Signup and view all the answers

What is the standard form of a circle's equation that allows the identification of its center?

<p>(x - a)^2 + (y - b)^2 = r^2 (A)</p> Signup and view all the answers

What is the condition for two polygons to be similar?

<p>All pairs of corresponding angles are equal, and all pairs of corresponding sides are in the same proportion (B)</p> Signup and view all the answers

How is the area of a triangle calculated using its base and height?

<p>Area = (1/2) × base × height (D)</p> Signup and view all the answers

What is the formula for the area of a triangle?

<p>Area = 1/2 × base × height (D)</p> Signup and view all the answers

What characterizes a polygon?

<p>It is constructed from at least three line segments. (B)</p> Signup and view all the answers

What is the regression coefficient (r) used for?

<p>To measure the strength of correlation between two sets of data (A)</p> Signup and view all the answers

What is the converse of the Pythagorean theorem used for?

<p>To prove a triangle is right-angled (C)</p> Signup and view all the answers

What is the condition for two triangles to have areas proportional to their bases?

<p>They have equal heights (C)</p> Signup and view all the answers

What is the advantage of using the linear regression line?

<p>It is used to make predictions based on a set of data (A)</p> Signup and view all the answers

If two triangles are equiangular, what can be concluded about their corresponding sides?

<p>They are in proportion (B)</p> Signup and view all the answers

What is the condition that must be met for two polygons to be determined as similar?

<p>All pairs of corresponding angles must be equal. (B)</p> Signup and view all the answers

According to the Mid-point Theorem, what is true about the line joining the midpoints of two sides of a triangle?

<p>It is parallel to the third side and half its length. (B)</p> Signup and view all the answers

Which of the following statements is true about equiangular triangles?

<p>Their corresponding sides are in proportion. (D)</p> Signup and view all the answers

If a triangle has a base of 4 cm and a height of 10 cm, what is its area?

<p>20 cm² (A)</p> Signup and view all the answers

In the statement of the Proportion Theorem, what must be true if a line is drawn parallel to one side of a triangle?

<p>It divides the other two sides proportionally. (C)</p> Signup and view all the answers

What can be concluded about two triangles if their corresponding sides are in proportion?

<p>They must be similar. (B)</p> Signup and view all the answers

Which condition is NOT necessary to prove that two triangles are similar?

<p>All sides are of equal length. (B)</p> Signup and view all the answers

What does the converse of the Mid-point Theorem state?

<p>If a line bisects a side, it is parallel to another side. (D)</p> Signup and view all the answers

In which situation would the two triangles riangle ABC and riangle DEF be considered similar?

<p>If all pairs of corresponding sides are in the same proportion. (C)</p> Signup and view all the answers

Which of the following is a characteristic of similar triangles?

<p>They have the same shape. (C)</p> Signup and view all the answers

What is the simplified form of the double angle formula for sine?

<p>$\sin(2\alpha) = 2\sin(\alpha)\cos(\alpha)$ (D)</p> Signup and view all the answers

Which of the following is NOT a valid form of the double angle formula for cosine?

<p>$\cos(2\alpha) = \sin^2(\alpha) + \cos^2(\alpha)$ (B)</p> Signup and view all the answers

What is the value of (\sin(2\alpha)) if (\sin(\alpha) = \frac{3}{5}) and (\alpha) is in the first quadrant?

<p>$\frac{24}{25}$ (B)</p> Signup and view all the answers

What is the value of (\cos(2\alpha)) if (\cos(\alpha) = \frac{1}{3}) and (\alpha) is in the first quadrant?

<p>$\frac{7}{9}$ (C)</p> Signup and view all the answers

Which of the following steps is NOT involved in finding the general solution of a trigonometric equation?

<p>Solve the equation for the unknown variable and then find its value in the given interval (B)</p> Signup and view all the answers

Which of the following trigonometric identities can be used to prove the double angle formula for cosine, (\cos(2\alpha) = \cos^2(\alpha) - \sin^2(\alpha))?

<p>$\cos(\alpha + \beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta)$ (C)</p> Signup and view all the answers

What is the general solution of the equation (\sin(x) = \frac{1}{2})?

<p>$\x = 30^\circ + 360^\circ k$ or $\x = 150^\circ + 360^\circ k$, where (k) is any integer (A)</p> Signup and view all the answers

Which of the following is NOT a valid step in deriving the double angle formula for sine?

<p>Use the Pythagorean identity (\sin^2(\alpha) + \cos^2(\alpha) = 1) to simplify the expression (C)</p> Signup and view all the answers

Which of the following trigonometric identities can be used to derive the alternate form of the double angle formula for cosine, (\cos(2\alpha) = 2\cos^2(\alpha) - 1)?

<p>$\sin^2(\alpha) + \cos^2(\alpha) = 1$ (B)</p> Signup and view all the answers

What is the value of (\cos(2\alpha)) if (\sin(\alpha) = \frac{4}{5}) and (\alpha) is in the first quadrant?

<p>$\frac{7}{25}$ (A)</p> Signup and view all the answers

What does a correlation coefficient of -0.5 indicate in terms of the relationship between two variables?

<p>There is a moderate negative correlation. (C)</p> Signup and view all the answers

Which of the following correctly represents the equation of a circle centered at the origin with a radius of 4?

<p>x^2 + y^2 = 16 (A)</p> Signup and view all the answers

In the equation of a regression line, what does the variable 'A' represent?

<p>The y-intercept. (D)</p> Signup and view all the answers

Which correlation coefficient value indicates a perfect positive correlation?

<p>r = 1 (D)</p> Signup and view all the answers

What is the interpretation of a correlation value of 0.3?

<p>A weak positive correlation. (D)</p> Signup and view all the answers

How is the linear correlation coefficient, r, calculated from the gradient of the least squares regression line?

<p>r = b (σ_x / σ_y) (D)</p> Signup and view all the answers

Which of the following structures is indicative of a strong negative correlation?

<p>-0.8 to -1 (D)</p> Signup and view all the answers

What does the equation y = A + Bx describe?

<p>A linear relationship between two variables. (C)</p> Signup and view all the answers

What is the value of r when there is a perfect negative correlation?

<p>-1 (B)</p> Signup and view all the answers

What is the outcome of equating the distance formula with the cosine rule for points on the unit circle?

<p>It leads to the expression for $ heta$ in sine and cosine. (A)</p> Signup and view all the answers

Which identity correctly defines $ ext{cos}( heta + eta)$ using the negative angle identity?

<p>$ ext{cos}( heta + eta) = ext{cos}( heta) ext{cos}(eta) - ext{sin}( heta) ext{sin}(eta)$ (A)</p> Signup and view all the answers

Which of the following transformations represents the cosine difference formula?

<p>$ ext{cos}( heta - eta) = ext{cos}( heta) ext{cos}(eta) + ext{sin}( heta) ext{sin}(eta)$ (D)</p> Signup and view all the answers

What does the equation $ ext{cos}( heta - eta) = ext{cos}( heta) ext{cos}(eta) + ext{sin}( heta) ext{sin}(eta)$ signify about the relationship between cosine and sine?

<p>It reveals the coexistence of sine and cosine in representing angle differences. (C)</p> Signup and view all the answers

Which identity correctly showcases the even-odd properties of trigonometric functions applied to cosine and sine?

<p>$ ext{cos}(-eta) = ext{cos}(eta)$ and $ ext{sin}(-eta) = - ext{sin}(eta)$ (A)</p> Signup and view all the answers

What is the result of substituting the even-odd identities for sine and cosine into the expression for $ ext{cos}( heta + eta)$?

<p>$ ext{cos}( heta + eta) = ext{cos}( heta) ext{cos}(eta) - ext{sin}( heta) ext{sin}(eta)$ (D)</p> Signup and view all the answers

If sinsθ = x, what is the general solution for θ?

<p>θ = sins^-1 x + k ⋅ 360° (C)</p> Signup and view all the answers

In a triangle ABC, which rule would be used to find the side a if the sides b and c and angle A are given?

<p>Cosine Rule (C)</p> Signup and view all the answers

What is the general approach for solving problems in three dimensions?

<p>Draw a sketch, consider the given information, apply appropriate rules, and calculate the desired quantities (C)</p> Signup and view all the answers

In a triangle ABC, if the area of the triangle is given by (1/2)bc sin A, what is the other way to express the area?

<p>(1/2)ab sin C (A)</p> Signup and view all the answers

What is the formula for the height of a pole in three dimensions?

<p>h = d sin α / sin β (C)</p> Signup and view all the answers

What is the formula for the height of a building in three dimensions?

<p>h = b sin α sin θ / sin (β + θ) (B)</p> Signup and view all the answers

If cos θ = x, what is the general solution for θ?

<p>θ = cos^-1 x + k ⋅ 360° (B)</p> Signup and view all the answers

If tan θ = x, what is the general solution for θ?

<p>θ = tan^-1 x + k ⋅ 90° (A)</p> Signup and view all the answers

What is the equation of a circle with center at the origin and radius 5?

<p>x^2 + y^2 = 25 (A)</p> Signup and view all the answers

What does a correlation value of -0.75 indicate?

<p>Moderate negative correlation (B)</p> Signup and view all the answers

What is the formula to calculate the cosine of a difference in trigonometry?

<p>cos(α - β) = cos α cos β + sin α sin β (D)</p> Signup and view all the answers

What is the formula for calculating the gradient (slope) of the least squares regression line?

<p>b = (Σxy - (Σx)(Σy) / n) / (Σx^2 - (Σx)^2 / n) (B)</p> Signup and view all the answers

Which of the following values represents a strong positive correlation?

<p>0.85 (B)</p> Signup and view all the answers

What is the interpretation of a very strong negative correlation?

<p>As x increases, y decreases significantly. (D)</p> Signup and view all the answers

What does a correlation value of 0 indicate?

<p>No correlation (A)</p> Signup and view all the answers

What is the formula for the sine of a sum in trigonometry?

<p>sin(α + β) = sin α cos β + cos α sin β (C)</p> Signup and view all the answers

Which of the following represents the equation of the regression line?

<p>y = A + Bx (A)</p> Signup and view all the answers

What is the value of the linear correlation coefficient 'r' when there is a perfect negative correlation?

<p>-1 (A)</p> Signup and view all the answers

If two triangles are similar, which of the following must be true?

<p>Corresponding angles are equal and corresponding sides are in proportion. (D)</p> Signup and view all the answers

What is the converse of the Mid-point Theorem?

<p>The line drawn from the midpoint of one side of a triangle bisects the third side of the triangle. (D)</p> Signup and view all the answers

What is the condition for two polygons to be similar?

<p>All pairs of corresponding angles are equal and all pairs of corresponding sides are in proportion. (C)</p> Signup and view all the answers

What is the formula for the area of a triangle?

<p>Area = (base × height) / 2 (B)</p> Signup and view all the answers

What is the statement of the Proportion Theorem?

<p>If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. (C)</p> Signup and view all the answers

What is true about equiangular triangles?

<p>They are similar. (B)</p> Signup and view all the answers

What is the condition for two triangles to have areas proportional to their bases?

<p>They are similar. (A)</p> Signup and view all the answers

What is the theorem that states that triangles with equal heights have areas proportional to their bases?

<p>None of the above (D)</p> Signup and view all the answers

What is the expression for the cosine of a difference in trigonometry?

<p>$\cos \alpha \cos eta + \sin \alpha \sin eta$ (A)</p> Signup and view all the answers

What is the expression for the cosine of a sum in trigonometry?

<p>$\cos \alpha \cos eta - \sin \alpha \sin eta$ (A)</p> Signup and view all the answers

What is the definition of similar polygons?

<p>Polygons with the same shape but not necessarily the same size. (B)</p> Signup and view all the answers

What is the relationship between the gradient of the radius and the gradient of the tangent at the point of tangency?

<p>m_radius × m_tangent = -1 (B)</p> Signup and view all the answers

How can the cosine of a sum be derived?

<p>Using the negative angle identity and the even-odd identities (B)</p> Signup and view all the answers

In a triangle, if a line is drawn parallel to one side, what happens to the other two sides?

<p>They are divided in the same ratio (C)</p> Signup and view all the answers

How do you prove two triangles are similar?

<p>By showing all corresponding angles are equal and all corresponding sides are in proportion. (A)</p> Signup and view all the answers

What is the advantage of using the cosine of a difference formula?

<p>It can be used to find the cosine of a difference (B)</p> Signup and view all the answers

What is the formula for the area of a triangle?

<p>Area = 1/2 × base × height (B)</p> Signup and view all the answers

What is a polygon?

<p>A plane, closed shape consisting of three or more line segments (B)</p> Signup and view all the answers

What is the cosine rule used for?

<p>Finding the distance between two points (A)</p> Signup and view all the answers

What is the relationship between the cosine of a difference and the cosine of a sum?

<p>They are equal (B)</p> Signup and view all the answers

What is the property of proportion that states w × z = x × y?

<p>Cross Multiplication (D)</p> Signup and view all the answers

If two ratios are equal, what can be concluded about the quantities involved?

<p>They are in proportion (B)</p> Signup and view all the answers

What is the condition for two triangles to be similar?

<p>They have proportional corresponding sides (A)</p> Signup and view all the answers

What is the formula for the equation of a circle with center (a, b) and radius r?

<p>(x - a)^2 + (y - b)^2 = r^2 (B)</p> Signup and view all the answers

What is the purpose of the Basic Proportionality Theorem?

<p>To divide the other two sides of a triangle proportionally (D)</p> Signup and view all the answers

What is the result of cross multiplying two ratios?

<p>An equation is formed (B)</p> Signup and view all the answers

If (\sin \theta = x), what is (\theta) equal to?

<p>(\theta = \sin^{-1} x + k \cdot 360^\circ) (B), (\theta = \sin^{-1} x + k \cdot 180^\circ) (D)</p> Signup and view all the answers

What is the formula for the area of a triangle:

<p>(\frac{1}{2}ac \sin B) (A), (\frac{1}{2}ab \sin C) (B), (\frac{1}{2}bc \sin A) (C)</p> Signup and view all the answers

When would you use the cosine rule?

<p>When no right angle is given, and either two sides and the included angle or three sides are given. (B)</p> Signup and view all the answers

What is the formula for the height of a pole?

<p>(h = \frac{d \sin \alpha}{\sin \beta} \tan \beta) (C)</p> Signup and view all the answers

What is the general approach to solving three-dimensional problems?

<p>Draw a sketch, consider the given information, apply appropriate rules, and calculate the desired quantities. (A)</p> Signup and view all the answers

What is the formula for the height of a building?

<p>(h = \frac{b \sin \alpha \sin \theta}{\sin(\beta + \theta)}) (A)</p> Signup and view all the answers

When would you use the sine rule?

<p>When no right angle is given, and either two sides and an angle (not the included angle) or two angles and a side are given. (D)</p> Signup and view all the answers

What is the formula for the area of a triangle in terms of its sides?

<p>(\sqrt{s(s-a)(s-b)(s-c)}) (D)</p> Signup and view all the answers

What is the area of a parallelogram with a base of 10 cm and a height of 4 cm?

<p>40 cm² (A)</p> Signup and view all the answers

Which of the following formulas correctly represents the area of a trapezium?

<p>Area = (1/2) × (base₁ + base₂) × height (D)</p> Signup and view all the answers

What can be concluded if two triangles are equiangular?

<p>Their corresponding sides are proportional. (B)</p> Signup and view all the answers

If a triangle has bases of 6 cm and 8 cm, and a height of 5 cm, what is the area of the triangle?

<p>25 cm² (B)</p> Signup and view all the answers

What distinguishes a kite from a rhombus?

<p>Kites do not need to have equal angles, while rhombuses do. (D)</p> Signup and view all the answers

What theorem states that triangles with the same base and height have equal areas?

<p>Triangle Area Theorem (C)</p> Signup and view all the answers

How is the area of a rectangle calculated?

<p>Area = length × width (A)</p> Signup and view all the answers

What is Thales' Theorem related to triangle proportions?

<p>A line parallel to a side divides the other two sides proportionally. (B)</p> Signup and view all the answers

If the diagonals of a rhombus are 10 cm and 24 cm, what is its area?

<p>120 cm² (D)</p> Signup and view all the answers

Which statement is true about the bases of a trapezium?

<p>The height is the distance between the bases. (A)</p> Signup and view all the answers

What is the standard equation of a circle with center at the point (a, b) and radius r?

<p>$(x - a)^2 + (y - b)^2 = r^2$ (B)</p> Signup and view all the answers

What step is performed first when completing the square for the equation of a circle in general form?

<p>Group the x and y terms (A)</p> Signup and view all the answers

If the equation of a circle is written as $(x - 3)^2 + (y + 2)^2 = 25$, what is the center of the circle?

<p>(3, -2) (B)</p> Signup and view all the answers

What does the tangent line to a circle represent?

<p>A line that touches the circle at exactly one point (D)</p> Signup and view all the answers

Given the general equation of a circle $x^2 + y^2 + 4x - 8y + 4 = 0$, what is the value of the radius?

<p>2 (A)</p> Signup and view all the answers

Which statement correctly describes the relationship between the radius and the tangent at the point of tangency on a circle?

<p>The radius forms a right angle with the tangent (A)</p> Signup and view all the answers

From the equation $x^2 + y^2 - 6x + 8y + 9 = 0$, what is the center of the circle?

<p>(3, 4) (B)</p> Signup and view all the answers

What formula is used to derive the radius when converting the general form of a circle's equation?

<p>$r = ext{sqrt}igg{igg(}rac{D}{2}igg)^2 + igg(rac{E}{2}igg)^2 - Figg{igg)}$ (A)</p> Signup and view all the answers

Which of the following correctly represents the sine of a difference formula?

<p>$ ext{sine}( heta - eta) = ext{sine} heta ext{cos} eta - ext{cos} heta ext{sine} eta$ (A)</p> Signup and view all the answers

What is the cosine of a sum formula?

<p>$ ext{cos}(eta + heta) = ext{cos} eta ext{cos} heta - ext{sin} eta ext{sin} heta$ (C)</p> Signup and view all the answers

Which identity is correctly derived for the sine of double angle?

<p>$ ext{sine}(2 heta) = 2 ext{cos} heta ext{sine} heta$ (D)</p> Signup and view all the answers

What is one form of the cosine of double angle?

<p>$ ext{cos}(2 heta) = ext{cos}^2 heta - ext{sin}^2 heta$ (A)</p> Signup and view all the answers

Which step is NOT part of the general solution method for solving trigonometric equations?

<p>Determining the values of the function for negative angles. (D)</p> Signup and view all the answers

The sine of a sum formula states:

<p>$ ext{sine}( heta + eta) = ext{sine} heta ext{cos} eta + ext{cos} heta ext{sine} eta$ (A)</p> Signup and view all the answers

To find the cosine of a difference, which formula is utilized?

<p>$ ext{cos}( heta - eta) = ext{cos} heta ext{cos} eta - ext{sin} heta ext{sin} eta$ (B)</p> Signup and view all the answers

What does the term reference angle refer to in trigonometric solutions?

<p>The angle in the first quadrant corresponding to the given angle. (A)</p> Signup and view all the answers

Which of the following represents a correct form of the sine double angle identity?

<p>$ ext{sine}(2 heta) = 2 ext{sine} heta ext{cos} heta$ (C)</p> Signup and view all the answers

In the context of similar triangles, what is the significance of the proportionality of corresponding sides?

<p>It allows us to determine the ratio of the areas of the triangles. (D)</p> Signup and view all the answers

Which of the following is NOT a condition for two polygons to be similar?

<p>The polygons have the same area. (C)</p> Signup and view all the answers

In the proof of the Pythagorean theorem, why are triangles ABD and CBA similar?

<p>They have all three corresponding angles equal. (B)</p> Signup and view all the answers

What is the relationship between the area of two triangles with equal bases but different heights?

<p>The areas are proportional to their heights. (D)</p> Signup and view all the answers

What is the purpose of the linear regression line in statistics?

<p>To predict the value of one variable based on the value of another variable. (A)</p> Signup and view all the answers

What is the meaning of a regression coefficient 'r' value close to +1?

<p>A strong positive correlation between the variables. (A)</p> Signup and view all the answers

Which of the following statements accurately describes the relationship between the Pythagorean theorem and right-angled triangles?

<p>The theorem relates the lengths of the sides of a right-angled triangle to each other. (B)</p> Signup and view all the answers

In the context of triangle proportionality, if a line is drawn parallel to one side of a triangle, what happens to the other two sides?

<p>The other two sides are divided in the same ratio. (B)</p> Signup and view all the answers

Which of the following is NOT a property of similar polygons?

<p>They have the same area. (D)</p> Signup and view all the answers

If two triangles are equiangular, what can be concluded about their corresponding sides?

<p>The corresponding sides are proportional. (B)</p> Signup and view all the answers

What is the equation of a circle with center (2, -3) and radius 4?

<p>(x - 2)^2 + (y + 3)^2 = 16 (C)</p> Signup and view all the answers

What are the coordinates of the center of the circle defined by the equation x^2 + y^2 - 6x + 4y - 12 = 0?

<p>(3, -2) (C)</p> Signup and view all the answers

What is the radius of the circle defined by the equation x^2 + y^2 + 8x - 10y + 25 = 0?

<p>3 (A)</p> Signup and view all the answers

A tangent line to a circle is always perpendicular to which of the following?

<p>The radius at the point of tangency (C)</p> Signup and view all the answers

Which of the following statements accurately describes the relationship between a tangent line and a radius at the point of tangency?

<p>They are perpendicular lines. (B)</p> Signup and view all the answers

What is the equation of the line that is tangent to the circle with the equation (x - 1)^2 + (y + 2)^2 = 9 at the point (4, 1)?

<p>y = -2x + 9 (D)</p> Signup and view all the answers

What is the gradient of the tangent line to the circle with equation (x + 3)^2 + (y - 2)^2 = 16 at the point (-1, 6)?

<p>-2 (C)</p> Signup and view all the answers

What is the equation of the tangent to the circle (x - 2)^2 + (y + 1)^2 = 25 at the point (7, -4)?

<p>y = -3x + 17 (A)</p> Signup and view all the answers

What is the formula for the area of a parallelogram?

<p>base × height (B)</p> Signup and view all the answers

If two triangles are similar, what can be concluded about their corresponding angles?

<p>They are equal (D)</p> Signup and view all the answers

What is the condition for two triangles to have areas proportional to their bases?

<p>They have equal heights (B)</p> Signup and view all the answers

What is the formula for the area of a kite?

<p>(diagonal AC × diagonal BD) / 2 (D)</p> Signup and view all the answers

What is the statement of the Basic Proportionality Theorem?

<p>If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. (B)</p> Signup and view all the answers

What is the formula for the area of a trapezium (trapezoid)?

<p>(base1 + base2) × height / 2 (B)</p> Signup and view all the answers

What is the statement of the Mid-point Theorem?

<p>A line joining the midpoints of two sides of a triangle is parallel to the third side and equal to half the length of the third side. (B)</p> Signup and view all the answers

What is the formula for the area of a rectangle?

<p>length × width (B)</p> Signup and view all the answers

What is the statement of the Proportion Theorem?

<p>A line drawn parallel to one side of a triangle divides the other two sides proportionally. (C)</p> Signup and view all the answers

What is the condition for two triangles to be similar?

<p>They are equiangular (D)</p> Signup and view all the answers

Given the equation of a circle: ( (x - 2)^2 + (y + 1)^2 = 9 ), what is the gradient of the tangent at the point (5, 1)?

<p>-3/2 (C)</p> Signup and view all the answers

In a triangle ABC, a line DE is drawn parallel to BC, dividing AB in the ratio 2:3. If AD = 8 cm, what is the length of DB?

<p>12 cm (D)</p> Signup and view all the answers

If the gradient of the radius of a circle is (\frac{1}{2}), what is the gradient of the tangent at the point of tangency?

<p>-2 (C)</p> Signup and view all the answers

Which of the following properties is NOT a property of proportions?

<p>Sum of Proportions: ( \frac{w + x}{y + z} = \frac{w}{y} = \frac{x}{z} ) (D)</p> Signup and view all the answers

What is the area of a triangle with a base of 10 cm and a height of 6 cm?

<p>30 cm (B)</p> Signup and view all the answers

If the equation of a tangent to a circle is ( y = 3x - 2 ), and the point of tangency is (1, 1), what is the gradient of the radius drawn to that point?

<p>-1/3 (D)</p> Signup and view all the answers

Given the equation of a circle: ( (x - 2)^2 + (y + 1)^2 = 9 ), what is the center of the circle?

<p>(2, -1) (A)</p> Signup and view all the answers

In a triangle ABC, a line DE is drawn parallel to BC, dividing AB in the ratio 2:1. If AD = 6 cm, what is the length of AB?

<p>9 cm (C)</p> Signup and view all the answers

Which of these is NOT a valid form of a ratio?

<p>2 + 3 (D)</p> Signup and view all the answers

Which of the following properties does NOT apply to similar polygons?

<p>Areas are equal. (D)</p> Signup and view all the answers

Which of the following is NOT a condition for two triangles to be similar?

<p>The areas of the triangles are equal. (B)</p> Signup and view all the answers

In the context of the Pythagorean Theorem, what is the relationship between the lengths of the sides of a right-angled triangle?

<p>The sum of the squares of the two shorter sides equals the square of the longest side. (D)</p> Signup and view all the answers

What does a regression coefficient (r) value close to -1 indicate?

<p>A strong negative correlation between the two sets of data. (D)</p> Signup and view all the answers

Which of the following statements accurately describes a property of similar triangles?

<p>They have the same shape but different sizes. (C)</p> Signup and view all the answers

In the proof of the Pythagorean Theorem, why are triangles ABD and CBA similar?

<p>They have three corresponding angles equal. (A)</p> Signup and view all the answers

Given two triangles with equal heights, how are their areas related?

<p>Their areas are in the ratio of their bases. (A)</p> Signup and view all the answers

What is the primary purpose of the linear regression line?

<p>To predict the value of one variable based on the value of another variable. (D)</p> Signup and view all the answers

What is the converse of the Pythagorean Theorem used for?

<p>To prove that a triangle is a right-angled triangle. (B)</p> Signup and view all the answers

Which of the following is a condition for polygons to be similar?

<p>All corresponding angles are equal and all corresponding sides are in proportion. (B)</p> Signup and view all the answers

If two triangles are equiangular, what can be concluded about their corresponding sides?

<p>Their corresponding sides are in proportion. (B)</p> Signup and view all the answers

What is the formula for the sine of a difference of two angles?

<p>$\sin(\alpha) \cos(\beta) - \cos(\alpha) \sin(\beta)$ (A)</p> Signup and view all the answers

What is the formula for the cosine of a sum of two angles?

<p>$\cos(\alpha + \beta) = \cos(\alpha) \cos(\beta) - \sin(\alpha) \sin(\beta)$ (D)</p> Signup and view all the answers

What is the formula for the sine of a double angle?

<p>$\sin(2\alpha) = 2 \sin(\alpha) \cos(\alpha)$ (B)</p> Signup and view all the answers

What is the formula for the cosine of a double angle?

<p>$\cos(2\alpha) = 2 \cos^2(\alpha) - 1$ (B), $\cos(2\alpha) = \cos^2(\alpha) - \sin^2(\alpha)$ (C)</p> Signup and view all the answers

What is the general approach to solving trigonometric equations?

<p>Use algebraic methods and trigonometric identities, then find reference angles and use the CAST diagram (B)</p> Signup and view all the answers

What is the purpose of the CAST diagram in solving trigonometric equations?

<p>To determine the sign of the trigonometric function (C)</p> Signup and view all the answers

What is the formula for the cosine of a difference of two angles?

<p>$\cos(\alpha - \beta) = \cos(\alpha) \cos(\beta) - \sin(\alpha) \sin(\beta)$ (B)</p> Signup and view all the answers

What is the formula for the sine of a sum of two angles?

<p>$\sin(\alpha + \beta) = \sin(\alpha) \cos(\beta) + \cos(\alpha) \sin(\beta)$ (A)</p> Signup and view all the answers

What is the purpose of the general solution method in solving trigonometric equations?

<p>To find all possible solutions to the equation (D)</p> Signup and view all the answers

What is the advantage of using trigonometric identities in solving trigonometric equations?

<p>They simplify the equation and make it easier to solve (A)</p> Signup and view all the answers

What is the correct expression derived from equating the distance formula and the cosine rule for two points on the unit circle?

<p>KL^2 = 2 - 2 ig(rac{1}{2}ig) (C)</p> Signup and view all the answers

Which identity allows the conversion of ext{cos}(eta - eta) during the derivation of ext{cos}(eta + eta)?

<p>Negative angle identities (D)</p> Signup and view all the answers

What formula is obtained from the cosine of a sum identity for angles ext{alpha} and ext{beta}?

<pre><code>ext{cos}( ext{alpha} + ext{beta}) = ext{cos} ext{alpha} ext{cos} ext{beta} + ext{sin} ext{alpha} ext{sin} ext{beta} (C) </code></pre> Signup and view all the answers

Using the distance formula, how can you express the distance KL between two points on the unit circle?

<p>KL^2 = ( ext{cos}( ext{alpha}) - ext{cos}( ext{beta}))^2 + ( ext{sin}( ext{alpha}) - ext{sin}( ext{beta}))^2 (C)</p> Signup and view all the answers

What is the main purpose of using the negative angle identity in the derivation process?

<p>To express ext{cos}(-eta) and ext{sin}(-eta) (B)</p> Signup and view all the answers

Which equation correctly reflects the relationship derived from the cosine rule related to angle differences on the unit circle?

<p>2 - 2 ext{cos}( ext{alpha} - ext{beta}) = 2 - 2 ( ext{cos} ext{alpha} ext{cos} ext{beta} + ext{sin} ext{alpha} ext{sin} ext{beta}) (C)</p> Signup and view all the answers

What is the formula to find the area of triangle ABC using the sides and an angle?

<p>Area = $\frac{1}{2}ac \sin B$ (A), Area = $\frac{1}{2}bc \sin A$ (C)</p> Signup and view all the answers

When is it appropriate to use the Sine Rule instead of the Cosine Rule?

<p>When two angles and the included side are known (A), When no right angle is given and two angles and a side are known (B)</p> Signup and view all the answers

Which equation correctly represents the Cosine Rule for side b?

<p>$b^2 = a^2 + c^2 - 2ac \cos B$ (C)</p> Signup and view all the answers

What type of problem would likely require the use of the Area Rule for triangles?

<p>When no perpendicular height is provided (C)</p> Signup and view all the answers

If \( an \theta = x\), what is the expression for (\theta)?

<p>(\theta = \tan^{-1} x + k \cdot 180^\circ) (C)</p> Signup and view all the answers

Which of the following accurately describes how to determine which trigonometric rule to apply to a triangle?

<p>Use the Area Rule when height is not provided. (D)</p> Signup and view all the answers

When calculating the height of a pole using triangles, which trigonometric function do you primarily apply?

<p>Tangent to find the height (A)</p> Signup and view all the answers

What does the formula (h = \frac{d \sin \alpha}{\sin \beta} \tan \beta) calculate?

<p>The height of a pole (A)</p> Signup and view all the answers

What does a correlation value of 0 indicate?

<p>There is no relationship between the variables. (D)</p> Signup and view all the answers

What is the equation of a circle with center at the origin and radius r?

<p>x^2 + y^2 = r^2 (D)</p> Signup and view all the answers

Which of the following statements is true for a strong negative correlation?

<p>As x increases, y decreases significantly. (A)</p> Signup and view all the answers

What does the linear correlation coefficient r range from?

<p>-1 to 1 (B)</p> Signup and view all the answers

How is the linear correlation coefficient r calculated?

<p>Using the formula: r = b(σ_x/σ_y) (C)</p> Signup and view all the answers

In terms of correlation strength, what does an r value of 0.3 indicate?

<p>Weak positive correlation (C)</p> Signup and view all the answers

What does the cosine of a sum formula describe?

<p>The relationship between cosine and sine of angles. (B)</p> Signup and view all the answers

Which of the following defines a perfect positive correlation?

<p>r = 1 (C)</p> Signup and view all the answers

What geometric shape's equation is given by x^2 + y^2 = r^2?

<p>Circle (A)</p> Signup and view all the answers

What is the interpretation of a weak positive correlation?

<p>As one variable increases, the other variable increases slightly. (B)</p> Signup and view all the answers

Two triangles are similar if they have the same shape but differ in size. This statement refers to which concept?

<p>Similar triangles (C)</p> Signup and view all the answers

A line drawn parallel to one side of a triangle divides the other two sides proportionally. This statement is the core of which theorem?

<p>Proportion theorem (B)</p> Signup and view all the answers

In a triangle ABC, a line DE is drawn parallel to BC, dividing AB in the ratio 2:3. If AD = 8 cm, what is the length of DB?

<p>6 cm (A)</p> Signup and view all the answers

If two triangles are equiangular, what can be concluded about their corresponding sides?

<p>They are proportional. (D)</p> Signup and view all the answers

Which of the following is NOT a condition for two polygons to be similar?

<p>All pairs of corresponding sides are equal. (B)</p> Signup and view all the answers

What is the formula for the area of a triangle?

<p>1/2 * base * height (C)</p> Signup and view all the answers

Which theorem states that a line joining the midpoints of two sides of a triangle is parallel to the third side and half its length?

<p>Mid-point Theorem (A)</p> Signup and view all the answers

If two triangles have equal bases between the same parallel lines, what can be concluded about their areas?

<p>Their areas are equal. (B)</p> Signup and view all the answers

What is the statement of the Converse of the Mid-point Theorem?

<p>If a line is drawn from the midpoint of one side of a triangle parallel to another side, it bisects the third side of the triangle. (C)</p> Signup and view all the answers

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