Congruent Angles

Vertical Angles Theorem Vertical angles are congruent.

Statements Reasons 1 and 2 are vertical angles GIVEN 1 and 2 are supplementary 2 and 3 are supplementary s in a linear pair Are supplementary m1 + m2 = 180 m2 + m3 = 180 Definition of Supplementary m1 + m2 = m2 + m3 Symmetric & Transitive m1 = m3 Subtraction Property 1  3 Definition of Congruent

SOME OTHER THEOREMS If 2 angles are supplementary to the same angle (or  s), then they are congruent.

If 2 angles are complementary to the same angle (or  s), , they are congruent.

All right angles are congruent.

If two angles are congruent and supplementary, then each is a right angle.

Remember Which angles are congruent. . Vertical  Remember Which angles are congruent?  Vertical  Supplementary to same  Complementary to same  All right angles