Podcast
Questions and Answers
What type of angle pair are ∠1 & ∠8?
What type of angle pair are ∠1 & ∠8?
- Alternate interior angles
- Corresponding angles (correct)
- Same-side interior angles
- Vertical angles
∠3 and ∠5 are same-side interior angles.
∠3 and ∠5 are same-side interior angles.
True (A)
Which angles are vertical angles?
Which angles are vertical angles?
∠3 & ∠10
If lines a and b are parallel, then ∠1 is _____ to ∠5.
If lines a and b are parallel, then ∠1 is _____ to ∠5.
Match each pair of angles to their classification:
Match each pair of angles to their classification:
Which of the following pairs of angles are a linear pair?
Which of the following pairs of angles are a linear pair?
If ∠7 is congruent to ∠13, then lines l and m must be parallel.
If ∠7 is congruent to ∠13, then lines l and m must be parallel.
If ∠3 and ∠13 are supplementary, this indicates that they are _____ together.
If ∠3 and ∠13 are supplementary, this indicates that they are _____ together.
What is the length of the altitude of an equilateral triangle with a side length of 10?
What is the length of the altitude of an equilateral triangle with a side length of 10?
The sine of angle A is equal to the ratio of the length of the opposite side to the length of the hypotenuse.
The sine of angle A is equal to the ratio of the length of the opposite side to the length of the hypotenuse.
What is the value of x to the nearest hundredth for the triangle with sides 11, 12, and x?
What is the value of x to the nearest hundredth for the triangle with sides 11, 12, and x?
For angle A in a right triangle, sin A = _____, cos A = _____, tan A = _____.
For angle A in a right triangle, sin A = _____, cos A = _____, tan A = _____.
What is the hypothesis in the statement 'If we won the division title, then we are in the playoffs'?
What is the hypothesis in the statement 'If we won the division title, then we are in the playoffs'?
The contrapositive of the statement 'If we won the division title, then we are in the playoffs' is 'If we are not in the playoffs, then we did not win the division title'.
The contrapositive of the statement 'If we won the division title, then we are in the playoffs' is 'If we are not in the playoffs, then we did not win the division title'.
What is the converse of the statement 'If we won the division title, then we are in the playoffs'?
What is the converse of the statement 'If we won the division title, then we are in the playoffs'?
If 5x − 5y = −3z and −3z = 5, then 5x − 5y = __________.
If 5x − 5y = −3z and −3z = 5, then 5x − 5y = __________.
Match the property with its definition:
Match the property with its definition:
Which property is illustrated by 'm∠1 + m∠2 = 180°' if ∠1 and ∠2 are supplementary?
Which property is illustrated by 'm∠1 + m∠2 = 180°' if ∠1 and ∠2 are supplementary?
For the property of reflexivity, it is true that if a = b, then b = a.
For the property of reflexivity, it is true that if a = b, then b = a.
If m∠2 = 9x + 28 and m∠3 = 47 - 2x, what do you find for x when m∠2 = m∠3?
If m∠2 = 9x + 28 and m∠3 = 47 - 2x, what do you find for x when m∠2 = m∠3?
If B is the midpoint of AC and AB = 2x – 3 and BC = 5x – 24, what value of x satisfies this equation?
If B is the midpoint of AC and AB = 2x – 3 and BC = 5x – 24, what value of x satisfies this equation?
If XB = 14 and XF = 20, then BF is equal to 34.
If XB = 14 and XF = 20, then BF is equal to 34.
Find the distance between the points A(-2, -4) and B(3, 8).
Find the distance between the points A(-2, -4) and B(3, 8).
If m∠3 = 27°, then m∠4 = _____.
If m∠3 = 27°, then m∠4 = _____.
What is the sum of m∠4 and m∠5 if OD bisects angle COE and OD ⊥ BF?
What is the sum of m∠4 and m∠5 if OD bisects angle COE and OD ⊥ BF?
Match each angle pair with their relationship:
Match each angle pair with their relationship:
If m∠FOD = 34°, then m∠GOB = _____.
If m∠FOD = 34°, then m∠GOB = _____.
If m∠BOD = (2x + 10)° and m∠1 = (3x - 10)°, find x if m∠BOD + m∠1 = 180°.
If m∠BOD = (2x + 10)° and m∠1 = (3x - 10)°, find x if m∠BOD + m∠1 = 180°.
The length of the third side of a triangle with sides 5 and 9 must be greater than _______ and less than _______.
The length of the third side of a triangle with sides 5 and 9 must be greater than _______ and less than _______.
Which of the following sets represent possible side lengths of a right triangle?
Which of the following sets represent possible side lengths of a right triangle?
A triangle with sides 6, 9, and 12 forms an obtuse triangle.
A triangle with sides 6, 9, and 12 forms an obtuse triangle.
What is the perimeter of a 30°, 60°, 90° triangle if the shorter leg is 8.3 inches long?
What is the perimeter of a 30°, 60°, 90° triangle if the shorter leg is 8.3 inches long?
Match the triangle classifications based on side lengths:
Match the triangle classifications based on side lengths:
In an isosceles triangle whose base is 10 and whose congruent sides are 9, the altitude can be calculated to find its length, which splits the base into two equal parts of ____ each.
In an isosceles triangle whose base is 10 and whose congruent sides are 9, the altitude can be calculated to find its length, which splits the base into two equal parts of ____ each.
If the bottom of a 13 ft ladder is 5 ft from the wall, how far up the wall does the ladder reach?
If the bottom of a 13 ft ladder is 5 ft from the wall, how far up the wall does the ladder reach?
What is the length of the cable reaching from the top of a 14 ft pole to a point on the ground 12 ft from the pole?
What is the length of the cable reaching from the top of a 14 ft pole to a point on the ground 12 ft from the pole?
If m∠12 = 67°, what is m∠8?
If m∠12 = 67°, what is m∠8?
If m∠6 = 108°, then m∠4 must be 72°.
If m∠6 = 108°, then m∠4 must be 72°.
If m∠13 = 123°, what is m∠12?
If m∠13 = 123°, what is m∠12?
If m∠1 = 2x + 7 and m∠16 = x + 30, find x: x = _____, m∠1 = _____, m∠16 = _____
If m∠1 = 2x + 7 and m∠16 = x + 30, find x: x = _____, m∠1 = _____, m∠16 = _____
If m∠2 = 11x - 16 and m∠7 = 7x + 28, find x.
If m∠2 = 11x - 16 and m∠7 = 7x + 28, find x.
Match the angles with their values based on given conditions:
Match the angles with their values based on given conditions:
What needs to be proved if a ∥ b and m ∥ n?
What needs to be proved if a ∥ b and m ∥ n?
In a right triangle, the sum of the angles is always 180 degrees.
In a right triangle, the sum of the angles is always 180 degrees.
What is the approximate value of x to the nearest tenth if the sides of the triangle are 11 and 12?
What is the approximate value of x to the nearest tenth if the sides of the triangle are 11 and 12?
In a right triangle, if angle A is 30 degrees, then sin A is equal to _____.
In a right triangle, if angle A is 30 degrees, then sin A is equal to _____.
Match the angles with their respective trigonometric ratios for angle A:
Match the angles with their respective trigonometric ratios for angle A:
Flashcards
Midpoint
Midpoint
The midpoint of a line segment divides the segment into two equal parts.
Distance Formula
Distance Formula
The distance between two points is calculated using the distance formula, which involves the square root of the sum of the squared differences of the x-coordinates and y-coordinates.
Angle Bisector
Angle Bisector
A line that bisects an angle divides the angle into two congruent angles.
Adjacent Angles
Adjacent Angles
Adjacent angles share a common vertex and a common side, but they do not overlap.
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Complementary Angles
Complementary Angles
Two angles are complementary if the sum of their measures is 90 degrees.
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Supplementary Angles
Supplementary Angles
Two angles are supplementary if the sum of their measures is 180 degrees.
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Vertical Angles
Vertical Angles
Two angles are vertical angles if they are opposite angles formed by the intersection of two lines.
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Right Angle
Right Angle
A right angle measures 90 degrees.
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Proposition
Proposition
A statement that can be true or false, but not both.
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Tautology
Tautology
A statement that is always true.
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Contradiction
Contradiction
A statement that is always false.
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Converse
Converse
The statement formed by switching the hypothesis and conclusion of a conditional statement.
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Inverse
Inverse
The statement formed by negating both the hypothesis and conclusion of a conditional statement.
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Contrapositive
Contrapositive
The statement formed by negating both the hypothesis and conclusion of a conditional statement and then switching them.
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Same-side interior angles
Same-side interior angles
Angles that are on the same side of the transversal and in between the parallel lines.
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Corresponding angles
Corresponding angles
Angles that are on the same side of the transversal but one is outside the parallel lines and one is inside.
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Alternate interior angles
Alternate interior angles
Angles that are on opposite sides of the transversal and inside the parallel lines.
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Alternate exterior angles
Alternate exterior angles
Angles that are on opposite sides of the transversal and outside the parallel lines.
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Congruent corresponding angles and parallel lines
Congruent corresponding angles and parallel lines
If two angles are congruent, then the lines are parallel.
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Supplementary same-side interior angles and parallel lines
Supplementary same-side interior angles and parallel lines
If two angles are supplementary, then the lines are parallel.
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Triangle Angle Sum Theorem
Triangle Angle Sum Theorem
The measures of all interior angles of a triangle add up to 180 degrees.
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Exterior Angle Theorem
Exterior Angle Theorem
The sum of the measures of the exterior angles of a triangle is 360 degrees.
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What is Sine?
What is Sine?
The trigonometric function sine (sin) of an angle is the ratio of the opposite side to the hypotenuse in a right triangle.
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What is Cosine?
What is Cosine?
The trigonometric function cosine (cos) of an angle is the ratio of the adjacent side to the hypotenuse in a right triangle.
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What is Tangent?
What is Tangent?
The trigonometric function tangent (tan) of an angle is the ratio of the opposite side to the adjacent side in a right triangle.
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What is the altitude of an equilateral triangle?
What is the altitude of an equilateral triangle?
The altitude of an equilateral triangle is the perpendicular line segment from a vertex to the opposite side.
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SOH CAH TOA
SOH CAH TOA
The trigonometric function sine (sin) of an angle is the ratio of the opposite side to the hypotenuse in a right triangle.
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Length of a Segment
Length of a Segment
The distance between the two ends of a line segment is called the length of the segment. If a segment is divided into two equal parts by a point, that point is called the midpoint of that segment.
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Altitude of a Triangle
Altitude of a Triangle
An altitude of a triangle is a line segment drawn from a vertex of the triangle perpendicular to the opposite side. This forms a 90 degree angle between the side and the altitude.
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Median of a Triangle
Median of a Triangle
A median of a triangle is a line segment drawn from a vertex of the triangle to the midpoint of the opposite side. The midpoint of the opposite side is the point where the median intersects it.
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Perpendicular Bisector
Perpendicular Bisector
A perpendicular bisector of a line segment is a line that cuts the segment into two equal parts and is perpendicular to the segment.
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Pythagorean Theorem
Pythagorean Theorem
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs).
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30-60-90 Triangle
30-60-90 Triangle
A 30-60-90 triangle is a special type of right triangle where the angles measure 30 degrees, 60 degrees, and 90 degrees. The sides of a 30-60-90 triangle have a specific ratio: the hypotenuse is twice the length of the shorter leg, and the longer leg is the square root of 3 times the length of the shorter leg.
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Isosceles Right Triangle
Isosceles Right Triangle
An isosceles right triangle is a right triangle where the two legs are congruent, which means they have the same length. The angles of an isosceles right triangle are 45 degrees, 45 degrees, and 90 degrees.
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Triangle Inequality Theorem
Triangle Inequality Theorem
The length of the third side of a triangle must be greater than the difference of the lengths of the other two sides and less than the sum of the lengths of the other two sides.
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Geometry Midterm Review 2024
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Unit 1: Basics of Geometry
- Midpoint Formula: If B is the midpoint of AC, AB = BC.
- Segment Addition Postulate: If X is between B and F, then XB + XF = BF.
- Angle Bisector: BD bisects ∠ABC, meaning ∠ABD = ∠DBC.
- Complementary and Supplementary Angles: Complementary angles add up to 90 degrees; supplementary angles add up to 180 degrees.
- Distance Formula: Used to find the distance between two points in a coordinate plane: √((x₂-x₁)² + (y₂-y₁)²).
- Midpoint Formula: Calculates the midpoint of a segment on a coordinate plane: ((x₁+x₂)/2, (y₁+y₂)/2).
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Geometry Matching
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Angles 21 and 22 are acute angles.
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Angles 21 and 25 are adjacent angles.
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Angles 24 and ∠AOD are adjacent angles.
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Angles 21 and ∠BOE are adjacent angles.
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Angles 21 and 26 are adjacent angles.
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∠AOC and ∠COE are adjacent angles.
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Further angle classification dependent on specific measurements.
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Unit 2: Logic and Reasoning
- Hypothesis: The part of a statement that comes after the "if".
- Conclusion: The part of a statement that comes after the "then".
- Converse: Switching the hypothesis and conclusion of a statement.
- Inverse: Negating both the hypothesis and conclusion of a statement.
- Contrapositive: Negating both the hypothesis and conclusion of the converse.
- Properties of Equality: Methods of manipulating equations (e.g., addition, subtraction, multiplication, division, distributive, reflexive).
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Unit 3: Parallel Lines and Transversals
- Corresponding Angles: Angles that are in the same position relative to their intersection with parallel lines; congruent if the lines are parallel.
- Alternate Interior Angles: Angles on opposite sides of the transversal and inside the parallel lines; congruent if the lines are parallel.
- Alternate Exterior Angles: Angles on opposite sides of the transversal and outside the parallel lines; congruent if the lines are parallel.
- Same-Side Interior Angles: Angles on the same side of the transversal and inside the parallel lines; supplementary if the lines are parallel.
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Unit 4: Triangle Properties
- Classifying Triangles: Based on side lengths (equilateral, isosceles, scalene) and angle measures (right, acute, obtuse, equiangular).
- Triangle Angle Sum Theorem: The sum of all the angles in a triangle is 180 degrees.
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Unit 5: Right Triangles
- Pythagorean Theorem: a² + b²= c² (relationship between lengths of the sides of a right triangle)
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Unit 6: Trigonometry
- Trigonometric Ratios: Sine, cosine, and tangent relate sides of a right triangle to angles; useful for calculating unknown lengths or angles.
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Problem Solving:
- Diagrams and figures are crucial for solving problems. Understanding postulates and theorems is core to success.
- Precise answers are needed.
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