Angle Relationship Proofs

Linear Pair Postulate

Angles which form linear pairs are supplementary.

Linear Pair Postulate

Vertical Angle Theorem

Vertical angles are congruent:

Vertical Angle Theorem

Vertical angles are congruent:

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

Statements Reasons

Given

Linear Pair Postulate

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.