# Theorem

A theorem is a true statement that can be proven.

- Congruence of Segments
- Segment congruence is reflexive, symmetric, and transitive.
- Reflexive - For any segment \(\;AB\; \), \(\;AB\; \)AB is congruent to \(\;AB\; \)
- Symmetric - If \(\;AB = CD\; \) , then \(\;CD = AB\; \)
- Transitive - If \(\;AB = CD\; \) and \(\;CD = EF\; \) . then \(\;AB = EF\; \)

- Segment congruence is reflexive, symmetric, and transitive.
- Congruent Angles
- Angle congruence is reflexive, symmetric, and transitive.
- Reflexive - For any \(\; \angle A\; \), \(\; \angle A\; = \angle A \)
- Symmetric - If \(\; \angle A = \angle B \; \) , then \(\; \angle B = \angle A \; \)
- Transitive - If \(\; \angle A = \angle B \; \) and \(\; \angle B = \angle C \; \), then \(\; \angle A = \angle C \; \)

- Angle congruence is reflexive, symmetric, and transitive.
- Right Angle Congruence
- All right angles are congruent.

- Congruent Supplements
- If two angles are supplementary to the same angle, then they are congruent.
- If two angles are supplementary to congruent angles, then they are congruent.

- Congruent Complementary
- If two angles are complementary to the same angle, then they are congruent.
- If two angles are complementary to congruent angles, then they are congruent.

- Vertical Angles Congruence
- Vertical angles are always congruent.