Geometry Definitions Used in Proofs

Study Notes

Definitions of Congruent Segments and Angles

Congruent segments have equal measures; if their lengths match, they are congruent.
Congruent angles also share the same measure; identical angle sizes indicate congruence.

Midpoints and Segment Bisectors

A midpoint divides a segment into two equal parts, each being a congruent segment.
A segment bisector (point, line, or ray) also creates two congruent segments from the original segment.

Types of Angles

Acute angles measure between 0 and 90 degrees.
Right angles are exactly 90 degrees.
Obtuse angles fall between 90 and 180 degrees.
Straight angles are precisely 180 degrees.

Angle Relationships

Angle bisectors divide an angle into two equal (congruent) angles.
Angle trisectors split an angle into three congruent angles.
Complementary angles have measures that sum to 90 degrees.
Supplementary angles have measures that sum to 180 degrees.

Linear Pairs

Two angles form a linear pair if they create a straight angle together, indicating their measures total 180 degrees.

Properties of Polygons

Equilateral polygons have all sides of equal length.
Equiangular polygons feature all angles being equal in measure.

Perpendicular Lines

Lines are perpendicular if they intersect at right angles (90 degrees).

Postulates

Segment Addition Postulate states that if point B is located between points A and C, then the sum of segments AB and BC equals segment AC.
Angle Addition Postulate indicates that if point P lies within angle RST, then the measure of angle RSP plus the measure of angle PST equals the measure of angle RST.

Description

This quiz features essential geometry definitions that are fundamental for understanding proofs. Key concepts like congruent segments and midpoints are explored, ensuring a firm grasp of foundational terms. Ideal for students looking to strengthen their geometry skills.