2.6 Geometric Proof Puzzles
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Given: π∠π ππ = π∠πππ Given: π∠πππ = π∠πππ Prove: π∠π ππ = 3(π∠π ππ) π∠π ππ = π∠πππ Given π∠πππ = π∠πππ Given π∠π ππ = π∠πππ Transitive Property π∠π ππ = π∠π ππ + π∠πππ + π∠πππ Angle Addition Postulate π∠π ππ = π∠π ππ + π∠π ππ + π∠π ππ Substitution Property π∠π ππ = 3(π∠π ππ) Simplify Given Simplify Transitive Property Substitution Angle Addition Given Given: PT = ER Prove: PE = TR PT = ER PT = PE + ET ER = ET + TR PE + ET = ET + TR ET = ET PE = TR Segment Addition Postulate Reflexive Property Subtraction Property Given Segment Addition Postulate Substitution Property Given: WX = YZ Prove: WY = XZ WX = YZ Given XY = XY Reflexive Property WX + XY = YZ + XY Addition Property WY = WX + XY Segment Addition Postulate XZ = YZ + XY Segment Addition Postulate WY = XZ Substitution Property Segment Addition Postulate Reflexive Property Addition Property Given Segment Addition Postulate Substitution Property Given: ∠π΄πΈπ΅ and ∠π΅πΈπΆ are complementary Given: ∠π΅πΈπΆ and ∠πΆπΈπ· are complementary Prove: ∠π΄πΈπ΅ ≅ ∠πΆπΈπ· ∠π΄πΈπ΅ and ∠π΅πΈπΆ are complementary Given ∠π΅πΈπΆ and ∠πΆπΈπ· are complementary Given π∠π΄πΈπ΅ + π∠π΅πΈπΆ = 90° Definition of Complementary Angles π∠π΅πΈπΆ + π∠πΆπΈπ· = 90° Definition of Complementary Angles π∠π΄πΈπ΅ + π∠π΅πΈπΆ = π∠π΅πΈπΆ + π∠πΆπΈπ· Substitution Property π∠π΄πΈπ΅ = π∠πΆπΈπ· Subtraction Property ∠π΄πΈπ΅ ≅ ∠πΆπΈπ· Definition of Congruent Angles Definition of Complimentary Angles Subtraction Property Definition of Congruent Angles Given Given Definition of Complimentary Angles Substitution Property Given: ∠1 and ∠2 form Linear Pair Given: ∠2 and ∠3 form Linear Pair Prove: ∠1 ≅ ∠3 Given ∠2 and ∠3 form Linear Pair Linear Pairs Theorem ∠2 and ∠3 are Supplementary Linear Pairs Theorem ∠1 + ∠2 = 180° ∠2 + ∠3 = 180° Definition of Supplementary Angles Substitution Property Subtraction Property ∠1 ≅ ∠3 Definition of Supplementary Angles ∠1 and ∠2 are Supplementary Given ∠1 = ∠3 Definition of Congruent Angles ∠1 + ∠2 = ∠2 + ∠3 ∠1 and ∠2 form Linear Pair Given: 5(π₯−2) 3 = 2(3π₯ − 4) Prove: π₯ = 1 5(π₯ − 2) = 2(3π₯ − 4) 3 Given 5π₯ − 10 = 2(3π₯ − 4) 3 Distributive Property 5π₯ − 10 = 6π₯ − 8 3 Distributive Property 5π₯ − 10 = 18π₯ − 24 Multiplication Property −10 = 12π₯ − 24 Subtraction Property 12 = 12π₯ Addition Property 1=π₯ Division Property Addition Property Subtraction Property Division Property Given Division Property Definition of Complimentary Angles Multiplication Property
