Theorem

Written by Jerry Ratzlaff. 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.