Transcript Angle Relationship Proofs
Angle Relationship Proofs
Linear Pair Postulate ο΅ Angles which form linear pairs are supplementary.
Linear Pair Postulate ο΅ πβ 1 + πβ 2 = 180Β° ο΅ πβ 2 + πβ 3 = 180Β°
Vertical Angle Theorem ο΅ Vertical angles are congruent: πβ 1 = πβ 3
Vertical Angle Theorem ο΅ Vertical angles are congruent: β 1 β β 3
Vertical Angle Theorem Proof ο΅ Given: Angles 1 and 2, and angles 2 and 3, are linear pairs.
ο΅ Prove: Angles 1 and 3 are congruent.
Vertical Angle Theorem Proof
Statements
β 1 & β 2 πππ π ππππππ ππππ; β 2 & β 3 πππ π ππππππ ππππ πβ 1 + πβ 2 = 180Β° πβ 3 + πβ 2 = 180Β° πβ 1 = πβ 3 β 1 β β 3
Reasons
Given Linear Pair Postulate Linear Pair Postulate Substitution Def. of Congruence
Corresponding Angle Postulate ο΅ If two lines crossed by a transversal are parallel, their corresponding angles are congruent.
Corresponding Angle Postulate
Other theorems ο΅ Using the Linear Pair Postulate and the Corresponding Angles Postulate, we can proveβ¦
Other theorems ο΅ Alt. Ext. Angles are Congruent ο΅ Alt. Int. Angles are Congruent
Other theorems ο΅ Same Side Ext. Angles are Supplementary ο΅ Same Side Int. Angles are Supplementary
Corresponding Angle Postulate ο΅ If two lines crossed by a transversal are parallel, their corresponding angles are congruent.
Converse of Corresponding Angles Postulate ο΅ If two lines crossed by a transversal have congruent corresponding angles, they are parallel.