Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships

Theorem 2.3: Right Angles Congruence Theorem All right angles are congruent.

Theorem 2.4: Congruent Supplements Theorem If two angles are supplementary to the same angle (or to congruent angles),then they are congruent.

Example If angles 1 and 3 are supplementary and angles 5 and 3 are supplementary, then angles 1 and 5 are congruent.

Theorem 2.5: Congruent Complements Theorem If two angles are complementary to the same angle (or to congruent angles),then they are congruent.

Example If angles 1 and 2 are complementary and angles 1 and 3 are complementary, then angles 2 and 3 are congruent.

Theorem 2.6: Vertical Angles Congruence Theorem Vertical angles are congruent.

Example

Postulate 12: Linear Pair Postulate If two angles form a linear pair, then they are supplementary.

Example Since angles 1 and 2 form a linear pair, they must be supplementary and m 1 + m 2 = 180º

Proof 1: Right Angles Congruence Theorem Given: PQR and UTS are right angles Prove: PQR UTS

StatementReason m PQR = 90º;2. m UTS = 90º m UTS = 90º 3.m PQR = m UTS Given: PQR and UTS are right angles Prove: PQR UTS

Example If m 1 = 112º, find the measure of angles 2, 3 & 4. If m 1 = 112º, find the measure of angles 2, 3 & 4.