Podcast
Questions and Answers
What is the term for a line, segment, or ray that is perpendicular to a segment at its midpoint?
What is the term for a line, segment, or ray that is perpendicular to a segment at its midpoint?
In an isosceles triangle, what is the angle that is different?
In an isosceles triangle, what is the angle that is different?
What is the longest side of a right triangle?
What is the longest side of a right triangle?
What is the term for a segment from a vertex to the midpoint of the opposite side?
What is the term for a segment from a vertex to the midpoint of the opposite side?
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What is the measure of a central angle to its intercepted arc?
What is the measure of a central angle to its intercepted arc?
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What is the term for a segment that is perpendicular to a segment at its endpoint?
What is the term for a segment that is perpendicular to a segment at its endpoint?
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If the ratio of the measures of the angles of a triangle is 2:2:5, what type of triangle is it?
If the ratio of the measures of the angles of a triangle is 2:2:5, what type of triangle is it?
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If each interior angle of a regular polygon is 144, how many sides does the polygon have?
If each interior angle of a regular polygon is 144, how many sides does the polygon have?
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In a 30° - 60° - 90° triangle, how many times the short leg is the long leg?
In a 30° - 60° - 90° triangle, how many times the short leg is the long leg?
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What is the sum of the exterior angles of a decagon?
What is the sum of the exterior angles of a decagon?
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If m ∠A is a right angle and m ∠A = (4x + 10)°, what is the value of x?
If m ∠A is a right angle and m ∠A = (4x + 10)°, what is the value of x?
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What type of angle is an angle inscribed in a semicircle?
What type of angle is an angle inscribed in a semicircle?
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If the length of the shorter leg of a 30°-60°-90° triangle is 5, then the length of the hypotenuse is
If the length of the shorter leg of a 30°-60°-90° triangle is 5, then the length of the hypotenuse is
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In the diagram, if AD = 2 and DB = 18, find CD.
In the diagram, if AD = 2 and DB = 18, find CD.
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Find the perimeter of a square whose area is 49.
Find the perimeter of a square whose area is 49.
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If the sides of a triangle are 5, 12, and 13, then the triangle is a
If the sides of a triangle are 5, 12, and 13, then the triangle is a
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If the length of the hypotenuse of a 45°-45°-90° triangle is 10, then the length of a leg is
If the length of the hypotenuse of a 45°-45°-90° triangle is 10, then the length of a leg is
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In the diagram, if m∠S = 90°, then sin T =
In the diagram, if m∠S = 90°, then sin T =
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Study Notes
Geometry Terms and Properties
- Reflexive property: a = a
- Transitive property: If a = b and b = c, then a = c
- Symmetric property: If a = b, then b = a
- Substitution property: If a = b, then a can be replaced by b in any expression
- Distributive property: a(b + c) = ab + ac
- Definition of midpoint: If D is the midpoint of AB, then AD = DB = 1/2AB
- Midpoint theorem: If D is the midpoint of AB, then AD = AB/2
- Segment addition postulate: If D is the midpoint of AB, then AD + DB = AB
- Right triangles: The longest side of a right triangle is the hypotenuse
- Similar triangles: Have congruent corresponding angles and proportional corresponding sides
- Isosceles triangles: Have two congruent sides and two congruent angles
- Equilateral triangles: Have all sides congruent and all angles congruent
- Altitude of a triangle: A segment from a vertex to the opposite side
- Median of a triangle: A segment from a vertex to the midpoint of the opposite side
- Bisector of a segment: A line, segment, or ray that divides the segment into two congruent parts
- Central angle: An angle whose vertex is the center of a circle
- Inscribed angle: An angle whose vertex is on a circle and whose sides contain chords of the circle
- Right angles: Two lines that form a 90° angle
- Collinear points: Three or more points that lie on the same line
- Coplanar points: Three or more points that lie in the same plane
Angles and Measurements
- Acute angles: Measure between 0° and 90°
- Right angles: Measure 90°
- Obtuse angles: Measure between 90° and 180°
- Straight angles: Measure 180°
- Interior angle sum of a hexagon: 720°
- Exterior angle sum of a decagon: 360°
- 30°-60°-90° triangle: The long leg is √3 times the short leg
- 45°-45°-90° triangle: The hypotenuse is √2 times the leg
- Angle inscribed in a semicircle: A right angle
Triangles and Congruence
- Congruent triangles: Have the same shape and size
- Similar triangles: Have the same shape but not necessarily the same size
- Triangle congruence theorems: SSS, SAS, ASA, AAS, HL
- Types of triangles: Equilateral, isosceles, scalene, right, obtuse, acute
Circles and Arcs
- Major arc: The longer arc between two points on a circle
- Minor arc: The shorter arc between two points on a circle
- Central angle: An angle whose vertex is the center of a circle
- Inscribed angle: An angle whose vertex is on a circle and whose sides contain chords of the circle
Geometry Formulas
- Area of a right triangle: 1/2(ab) = 1/2(base)(height)
- Perimeter of a square: 4s
- Diagonal of a square: s√2
- Area of a square: s^2
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Description
This quiz covers various geometry concepts, including properties of equality, midpoint theorems, and segment addition postulates.
