Honors Geometry Theorems and Definitions

Vocabulary and theorem flashcards derived from the Honors Geometry Theorems List.

Assumptions from a Diagram

The geometric properties you may assume directly from a diagram: straight lines and angles, collinearity of points, betweenness of points, and relative positions of points.

Right Angle Congruence Theorem

If two angles are right angles, then they are congruent.

Straight Angle Congruence Theorem

If two angles are straight angles, then they are congruent.

Right Angle

If an angle is a right angle, then its measure is $90$; conversely, if an angle has a measure of $90$, then it is a right angle.

Straight Angle

If an angle is a straight angle, then its measure is $180$; conversely, if an angle has a measure of $180$, then it is a straight angle.

Acute Angle

If an angle is an acute angle, then its measure is greater than $0$ and less than $90$; conversely, if an angle has a measure greater than $0$ and less than $90$, then it is an acute angle.

Obtuse Angle

If an angle is an obtuse angle, then its measure is greater than $90$ and less than $180$; conversely, if an angle has a measure greater than $90$ and less than $180$, then it is an obtuse angle.

Congruent Angles

If two angles are congruent, then they have the same measure; conversely, if two angles have the same measure, then they are congruent.

Congruent Segments

If two segments are congruent, then they have the same length; conversely, if two segments have the same length, then they are congruent.

Angle Bisector

If a ray bisects an angle, then it divides the angle into two congruent angles; conversely, if a ray divides an angle into two congruent angles, then it bisects the angle.

Segment Bisector

If a (point, line, ray, segment) bisects a segment, then it divides the segment into two congruent segments; conversely, if a (point, line, ray, segment) divides a segment into two congruent segments, then it bisects the segment.

Angle Trisectors

If two rays trisect an angle, then they divide the angle into three congruent angles; conversely, if two rays divide an angle into three congruent angles, then they trisect the angle.

Segment Trisectors

If two (points, lines, rays, segments) trisect a segment, then they divide the segment into three congruent segments; conversely, if two (points, lines, rays, segments) divide a segment into three congruent segments, then they trisect the segment.

Midpoint of a Segment

If a point is the midpoint of a segment, then it divides the segment into two congruent segments; conversely, if a point divides a segment into two congruent segments, then it is the midpoint of the segment.

Algebra Properties

The algebraic properties listed for geometric proofs, including Addition and Subtraction.