Gr 9 MATH: Ch9 Sum Geometry of 2D Shapes and Construction of Geometric Figures
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Questions and Answers

What is the definition of a regular polygon?

  • A polygon with all sides equal.
  • A polygon with only one right angle.
  • A polygon with all sides and angles equal. (correct)
  • A polygon with sides and angles not all equal.

What is the sum of interior angles in an equilateral triangle?

  • 180^\circ (correct)
  • 150^\circ
  • 210^\circ
  • 240^\circ

What is the formula for the area of a square?

  • A = s^2 (correct)
  • A = 2 imes s
  • A = l imes w
  • A = 4 imes s

What is the name of a polygon with only one right angle?

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

What is the formula for the perimeter of a rectangle?

<p>P = 2(l + w) (D)</p> Signup and view all the answers

What is the name of a quadrilateral with opposite sides parallel and equal?

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

What is the formula for the area of a circle?

<p>A = \pi r^2 (C)</p> Signup and view all the answers

What is the name of a portion of a circle defined by two radii and the arc between them?

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

What is the formula for the area of a sector in a circle?

<p>A = θ/360 × πr^2 (C)</p> Signup and view all the answers

What is the sum of the interior angles of a regular polygon with 8 sides?

<p>1200° (B)</p> Signup and view all the answers

What is the formula for the area of a regular polygon?

<p>A = 1/4 ns^2 cot(Ï€/n) (B)</p> Signup and view all the answers

What is the method for constructing a perpendicular line through a point not on the line segment?

<p>Draw two circles with the end points of the line segment as centers and passing through the given point. (D)</p> Signup and view all the answers

What is the method for bisecting an angle using circles?

<p>Draw a circle with the vertex of the angle as the center and marking off equal lengths on both arms of the angle. (A)</p> Signup and view all the answers

What is the angle formed by the intersection of two perpendicular lines?

<p>90° (A)</p> Signup and view all the answers

What is the criterion for congruency of two triangles?

<p>Two triangles are congruent if they have the same shape and size. (D)</p> Signup and view all the answers

What is the minimum condition for congruency of two triangles?

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

What is the property of the angle bisectors of a triangle?

<p>The three angle bisectors of a triangle intersect at one point, equidistant from each side of the triangle. (B)</p> Signup and view all the answers

What is the relationship between the exterior angle of a triangle and the interior opposite angles?

<p>The exterior angle of a triangle is equal to the sum of the interior opposite angles. (D)</p> Signup and view all the answers

What is the minimum condition for congruency of triangles?

<p>Three sides or three angles (C)</p> Signup and view all the answers

What is the formula for the area of a triangle?

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

Which of the following is not a condition for congruency of triangles?

<p>One side and one angle (D)</p> Signup and view all the answers

What is the formula for the perimeter of a rectangle?

<p>P = 2(l + w) (B)</p> Signup and view all the answers

What is the formula for the area of a circle?

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

How do you construct a triangle with two sides and an included angle?

<p>Draw the base, use a protractor to measure the given angle, then draw the other side and connect the vertices. (C)</p> Signup and view all the answers

What is the formula for the sum of interior angles of a regular polygon?

<p>Sum = (n - 2) × 180° (C)</p> Signup and view all the answers

What is the formula for the area of a sector?

<p>A = θ/360 × πr^2 (C)</p> Signup and view all the answers

How do you construct a rhombus?

<p>Use a compass to draw four equal sides from a single vertex, ensuring all sides are the same length. (A)</p> Signup and view all the answers

What is the formula for the diagonal of a rectangle?

<p>d = √(l^2 + w^2) (A)</p> Signup and view all the answers

What is the name of the figure formed by the intersection of two circles, each with one of its ends as the center?

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

If the interior angles of a regular polygon are each 120 degrees, how many sides does the polygon have?

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

What is the length of the diagonal of a rectangle with length 5 cm and width 3 cm?

<p>5.83 cm (A)</p> Signup and view all the answers

What is the name of the point where the three angle bisectors of a triangle intersect?

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

If two triangles have two pairs of congruent sides and the included angles are congruent, what can be concluded?

<p>The triangles are congruent (D)</p> Signup and view all the answers

What is the area of a sector with a radius of 4 cm and a central angle of 60 degrees?

<p>8.38 cm^2 (D)</p> Signup and view all the answers

If two triangles have three pairs of congruent sides, what can be concluded?

<p>The triangles are congruent (C)</p> Signup and view all the answers

What is the length of the arc of a circle with a radius of 5 cm and a central angle of 45 degrees?

<p>3.94 cm (D)</p> Signup and view all the answers

What is the name of the line that cuts an angle in half?

<p>Angle Bisector (C)</p> Signup and view all the answers

What is the sum of the interior opposite angles of an exterior angle of a triangle?

<p>The exterior angle (B)</p> Signup and view all the answers

What is the name of a polygon with all sides and angles equal?

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

What is the formula for the area of a parallelogram?

<p>A = b * h (B)</p> Signup and view all the answers

What is the name of a quadrilateral with opposite sides equal and parallel?

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

What is the sum of the interior angles of a triangle?

<p>180^\circ (B)</p> Signup and view all the answers

What is the formula for the circumference of a circle?

<p>C = 2 * pi * r (A)</p> Signup and view all the answers

What is the name of a triangle with two sides and two angles equal?

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

What is the formula for the area of a trapezium?

<p>A = 1/2 * (a + b) * h (B)</p> Signup and view all the answers

What is the name of a quadrilateral with all sides equal?

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

Which of the following methods can be used to construct a triangle, given two sides and an angle not included?

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

What is the formula for the area of a trapezium?

<p>A = (a + b) * h / 2 (C)</p> Signup and view all the answers

Which of the following is a necessary condition for two triangles to be congruent?

<p>All of the above (D)</p> Signup and view all the answers

What is the formula for the perimeter of a polygon with n sides, each of length s?

<p>P = n * s (A)</p> Signup and view all the answers

Which of the following shapes has an area that can be calculated using the formula A = πr^2?

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

What is the formula for the length of an arc of a circle, given the central angle θ in degrees and the radius r?

<p>L = θ / 360 * 2πr (C)</p> Signup and view all the answers

Which of the following methods can be used to construct a triangle, given one side and two angles?

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

What is the formula for the area of a parallelogram, given the base b and height h?

<p>A = b * h (C)</p> Signup and view all the answers

Which of the following is a property of the angle bisectors of a triangle?

<p>They intersect at the incenter (C)</p> Signup and view all the answers

What is the formula for the sum of the interior angles of a regular polygon with n sides?

<p>Sum = (n - 2) * 180 (D)</p> Signup and view all the answers

What is the unique property of a rhombus that is not true for all quadrilaterals?

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

What is the condition for a quadrilateral to be a parallelogram?

<p>Opposite sides are equal and parallel (B)</p> Signup and view all the answers

What is the formula for the area of a sector with radius r and central angle θ?

<p>A = (θ/360) × πr^2 (C)</p> Signup and view all the answers

What is the name of a triangle with three sides and three angles equal?

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

What is the condition for two triangles to be congruent?

<p>Two pairs of congruent sides and one pair of congruent angles (C)</p> Signup and view all the answers

What is the formula for the circumference of a circle with radius r?

<p>C = 2Ï€r (C)</p> Signup and view all the answers

What is the unique property of an isosceles triangle?

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

What is the formula for the perimeter of a rectangle with length l and width w?

<p>P = 2l + 2w (A)</p> Signup and view all the answers

What is the minimum condition for congruency of two triangles given one side and two angles?

<p>One side and two angles (A)</p> Signup and view all the answers

What is the formula for the area of a triangle with three sides a, b, and c?

<p>A = sqrt(s(s - a)(s - b)(s - c)) (B)</p> Signup and view all the answers

What is the method for constructing a triangle given two sides and an included angle?

<p>Draw the base and use a protractor to measure the given angle, then draw the other side and connect the vertices (D)</p> Signup and view all the answers

What is the formula for the perimeter of a polygon with n sides, each of length s?

<p>P = n * s (C)</p> Signup and view all the answers

What is the minimum condition for congruency of two triangles given two sides and an angle not included?

<p>Two sides and an angle not included (B)</p> Signup and view all the answers

What is the formula for the area of a parallelogram with base b and height h?

<p>A = b * h (A)</p> Signup and view all the answers

What is the method for constructing a circle with a given radius from a central point?

<p>Use a compass to draw a circle with a given radius from a central point (A)</p> Signup and view all the answers

What is the formula for the area of a sector with a radius of r and a central angle of θ?

<p>A = (θ / 360) * π * r^2 (A)</p> Signup and view all the answers

What is the minimum condition for congruency of two triangles given two angles and an included side?

<p>Two angles and an included side (D)</p> Signup and view all the answers

What is the formula for the circumference of a circle with a radius of r?

<p>C = 2 * π * r (A)</p> Signup and view all the answers

What is the relationship between the area of a sector and the angle of the sector?

<p>The area of a sector is directly proportional to the angle of the sector. (A)</p> Signup and view all the answers

What is the minimum number of conditions required to prove that two triangles are congruent?

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

What is the length of the arc of a circle with a radius of 6 cm and a central angle of 30 degrees?

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

What is the area of a regular polygon with 10 sides and side length 4 cm?

<p>160 cm^2 (D)</p> Signup and view all the answers

What is the relationship between the exterior angle of a triangle and the interior opposite angles?

<p>The exterior angle is equal to the sum of the interior opposite angles. (D)</p> Signup and view all the answers

What is the condition for two triangles to be congruent, given that they have two pairs of congruent sides and one pair of congruent angles?

<p>The included angle must be congruent. (B)</p> Signup and view all the answers

What is the formula for the perimeter of a regular polygon with n sides, each of length s?

<p>P = ns (A)</p> Signup and view all the answers

What is the point of intersection of the three angle bisectors of a triangle?

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

What is the method for constructing a 60° angle?

<p>Drawing an equilateral triangle and bisecting one of its angles (A)</p> Signup and view all the answers

What is the relationship between the diagonal of a rectangle and its sides?

<p>The diagonal is equal to the square root of the sum of the squares of the sides. (A)</p> Signup and view all the answers

What is the name of a quadrilateral with opposite sides equal, but not all angles equal?

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

What is the sum of interior angles of a triangle?

<p>180° (D)</p> Signup and view all the answers

What is the formula for the perimeter of a square with side length s?

<p>P = 4s (A)</p> Signup and view all the answers

What is the name of a polygon with all sides and angles not equal?

<p>Irregular Polygon (C)</p> Signup and view all the answers

What is the formula for the area of a circle with radius r?

<p>A = πr^2 (C)</p> Signup and view all the answers

What is the name of a triangle with one right angle?

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

What is the formula for the circumference of a circle with radius r?

<p>C = 2Ï€r (B)</p> Signup and view all the answers

What is the name of a quadrilateral with opposite sides parallel and equal?

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

What is the minimum condition for congruency of two triangles?

<p>SSS, SAS, ASA, and RHS (D)</p> Signup and view all the answers

What is the formula for the area of a triangle?

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

What is the formula for the perimeter of a quadrilateral?

<p>P = a + b + c + d (B)</p> Signup and view all the answers

What is the formula for the area of a circle?

<p>A = πr^2 (D)</p> Signup and view all the answers

What is the formula for the circumference of a circle?

<p>C = 2Ï€r (D)</p> Signup and view all the answers

What is the formula for the area of a sector?

<p>A = (θ/360) × πr^2 (D)</p> Signup and view all the answers

What is the formula for the area of a sector in a circle?

<p>$A = rac{ heta}{360} imes \pi r^2$ (D)</p> Signup and view all the answers

What is the method for constructing a triangle with two sides and an included angle?

<p>Use a protractor to measure the given angle, then draw the other side and connect the vertices. (D)</p> Signup and view all the answers

What is the formula for the perimeter of a polygon with $n$ sides, each of length $s$?

<p>$P = ns$ (C)</p> Signup and view all the answers

What is the formula for the perimeter of a polygon with n sides, each of length s?

<p>P = ns (C)</p> Signup and view all the answers

What is the method for constructing a 45 angle?

<p>Bisecting a 90 angle (A)</p> Signup and view all the answers

What is the method for constructing a rhombus?

<p>Use a compass to draw four equal sides from a single vertex, ensuring all sides are the same length. (D)</p> Signup and view all the answers

What is the property of the angle bisectors of a triangle?

<p>They intersect at a point equidistant from each side of the triangle (A)</p> Signup and view all the answers

What is the formula for the area of a parallelogram?

<p>A = b × h (D)</p> Signup and view all the answers

What is the formula for the arc length of a circle?

<p>$L = rac{ heta}{360} imes 2 \pi r$ (A)</p> Signup and view all the answers

What is the criterion for congruency of two triangles?

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

What is the minimum condition for congruency of two triangles?

<p>Two pairs of congruent sides and the included angles are congruent (D)</p> Signup and view all the answers

What is the relationship between the exterior angle of a triangle and the interior opposite angles?

<p>The exterior angle is equal to the sum of the interior opposite angles (A)</p> Signup and view all the answers

What is the formula for the area of a regular polygon?

<p>$A = rac{1}{4} n s^2 \cot(rac{\pi}{n})$ (A)</p> Signup and view all the answers

What is the method for constructing a perpendicular line through a point not on the line segment?

<p>Drawing a circle with one end point of the line segment as the center and passing through the given point (B)</p> Signup and view all the answers

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