Theorem

Written by Jerry Ratzlaff on . Posted in Algebra

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 $$\;AB = EF\;$$
• 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 $$\; \angle A = \angle C \;$$
• 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.