Angle Relationship Proofs

Linear Pair Postulate  Angles which form linear pairs are supplementary.

Linear Pair Postulate

Vertical Angle Theorem

Vertical Angle Theorem Proof  Given: Angles 1 and 2, and angles 2 and 3, are linear pairs.  Prove: Angles 1 and 3 are congruent.

Vertical Angle Theorem Proof StatementsReasons Given Linear Pair Postulate Substitution Def. of Congruence

Corresponding Angle Postulate  If two lines crossed by a transversal are parallel, their corresponding angles are congruent.

Corresponding Angle Postulate

Other theorems  Using the Linear Pair Postulate and the Corresponding Angles Postulate, we can prove…

Other theorems  Alt. Ext. Angles are Congruent  Alt. Int. Angles are Congruent

Other theorems  Same Side Ext. Angles are Supplementary  Same Side Int. Angles are Supplementary

Corresponding Angle Postulate  If two lines crossed by a transversal are parallel, their corresponding angles are congruent.

Converse of Corresponding Angles Postulate  If two lines crossed by a transversal have congruent corresponding angles, they are parallel.