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2-8 Proving Angle Relationships

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)

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2-8 Proving Angle Relationships

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  1. 2-8 Proving Angle Relationships Ms. Andrejko

  2. Real - World

  3. 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)

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

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

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

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

  8. Practice – Fill in the proof <QPS ≅ <TPR Def. of congruent Angle + Post. <QPR +<RPS = <TPS +<RPS <QPR= <TPS <QPR≅<TPS Def. of Congruent

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