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?
- altitude
- bisector
- perpendicular bisector (correct)
- median
In an isosceles triangle, what is the angle that is different?
In an isosceles triangle, what is the angle that is different?
- base angle
- leg angle
- vertical angle
- vertex angle (correct)
What is the longest side of a right triangle?
What is the longest side of a right triangle?
- base
- leg
- hypotenuse (correct)
- altitude
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?
What is the measure of a central angle to its intercepted arc?
What is the measure of a central angle to its intercepted arc?
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?
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?
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?
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?
What is the sum of the exterior angles of a decagon?
What is the sum of the exterior angles of a decagon?
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?
What type of angle is an angle inscribed in a semicircle?
What type of angle is an angle inscribed in a semicircle?
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
In the diagram, if AD = 2 and DB = 18, find CD.
In the diagram, if AD = 2 and DB = 18, find CD.
Find the perimeter of a square whose area is 49.
Find the perimeter of a square whose area is 49.
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
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
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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