2 8 Proving Angle Relationships Ms Andrejko Real

2 -8 Proving Angle Relationships Ms. Andrejko

Real - World

Postulates and Theorems � 2. 10 (Protractor Postulate) � 2. 11 (Angle addition Postulate) �Thrm: 2. 3 (Supplement) �Thrm: 2. 4 (Complement) �Thrm: 2. 5 (Angle congruence) �Thrm: 2. 6 (Congruent supplement) �Thrm: 2. 7 (Congruent complements) �Thrm: 2. 8 (Vertical angles) �Thrm: 2. 9 – 2. 13 (Right angle theorems)

Examples 1. <1 = x+10 X+10 + 3 x+18 = <2 = 3 x+18 180 4 x+28=180 4 x=152 X=38 Supplement Theorem 2. <4 = 2 x-5 <5 = 4 x-13 <3 = 90 <4 = 2(18)-5 = 31 <5 = 4(18)-13 = 59 <1 = x+10 = 38+10 = 48 <2 = 3(38)+18 = 132 2 x-5+4 x-13 = 90 6 x-18 = 90 6 x=108 X=18 Complement Theorem

Practice 1. <6 = 7 x-24 = 5 x+14 <7 = 5 x+14 2 x = 38 X = 19 Vertical <‘s Theorem <6 = 7(19)-24 = 109 <7 = 109 2. <5 = 22 90 -22 = 68 <6 = 68 Complement Theorem

Example/Practice <7 = 49 <8 = 41 <9 = 49 <10 = 41 90 -41 = 49 ≅ Complement Theorem

Example – Fill in the proof STATEMENTS <1 & <2 form a linear pair <2 &<3 are <1& <2 are supplementary <1 + < 2 = 180 REASONS given Def. of linear pair Def. ofofsupplementary Def. <2+<3 = 180 <1+<2=<2+<3 <1 = <3 Substitution <1 ≅ <3 Subtraction Def. of Congruence

Practice – Fill in the proof STATEMENTS REASONS a. <QPS ≅ <TPR <QPS = <TPR Given <QPS = <QPR +<RPS <TPR = <TPS + <RPS c. d. <QPR +<RPS = <TPS <QPR= <TPS e. +<RPS Substitution f. <QPR≅ <TPS b. Def. of congruent Angle + Post. Subtraction Def. of Congruent