geometry 2.7 big idea: prove angle pair big idea: prove angle pairrelationships
DESCRIPTION
Theorem 2.4: Congruent Supplements Theorem If two angles are supplementary to the same angle (or to congruent angles),then they are congruent.TRANSCRIPT
Geometry 2.7Geometry 2.7 Big Idea: Prove Big Idea: Prove
Angle PairAngle PairRelationshipsRelationships
Theorem 2.3:Theorem 2.3:Right Angles Right Angles Congruence TheoremCongruence Theorem
All right angles are All right angles are congruent.congruent.
Theorem 2.4:Theorem 2.4:Congruent Supplements Congruent Supplements TheoremTheorem
If two angles are If two angles are supplementary to the supplementary to the same angle (or to same angle (or to congruent angles),then congruent angles),then they are congruent.they are congruent.
ExampleExample
If angles 1 and 3 are supplementary and If angles 1 and 3 are supplementary and angles 5 and 3 are supplementary, angles 5 and 3 are supplementary, then angles 1 and 5 are congruent.then angles 1 and 5 are congruent.
Theorem 2.5:Theorem 2.5:Congruent Complements Congruent Complements TheoremTheorem
If two angles are If two angles are complementary to the complementary to the same angle (or to same angle (or to congruent angles),then congruent angles),then they are congruent.they are congruent.
ExampleExample11 2 32 3
If angles 1 and 2 are If angles 1 and 2 are complementary and angles 1 complementary and angles 1 and 3 are complementary, then and 3 are complementary, then angles 2 and 3 are congruent.angles 2 and 3 are congruent.
Theorem 2.6:Theorem 2.6:Vertical Angles Vertical Angles Congruence TheoremCongruence Theorem
Vertical angles are Vertical angles are congruent.congruent.
ExampleExample
4 24 2 1 3 1 3
Postulate 12:Postulate 12:Linear Pair PostulateLinear Pair PostulateIf two angles form a linear If two angles form a linear
pair, then they are pair, then they are supplementary.supplementary.
ExampleExample
Since angles 1 and 2 form a Since angles 1 and 2 form a linear pair, they must be linear pair, they must be supplementary and supplementary and m m 1 + 1 + mm 2 = 180 2 = 180ºº
Proof 1: Right Angles Proof 1: Right Angles Congruence TheoremCongruence Theorem
Given: PQR and UTS are right Given: PQR and UTS are right anglesangles
Prove: PQR UTSProve: PQR UTS
StatementStatement ReasonReason1. 1. 1.1.2. 2. mm PQR = 90 PQR = 90º;º; 2. 2. m m UTS = 90º UTS = 90º3.3.m m PQR = PQR = mm UTS UTS 3. 3. 4.4. 4.4.5.5. 5. 5.
Given: PQR and UTS are right anglesProve: PQR UTS
ExampleExample
If If mm 1 = 112 1 = 112º, find the º, find the measure of angles 2, 3 & 4.measure of angles 2, 3 & 4.