Geometry Final Exam Questions

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