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
<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
<6 = 7(19)-24 = 109
<7 = 109
Vertical <‘s Theorem
90-22 = 68
<6 = 68
Complement Theorem

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

7. Example – Fill in the proof
STATEMENTS
REASONS
given
<1& <2 are supplementary
Def. of supplementary
<2+<3 = 180
<1+<2=<2+<3
Subtraction
<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
STATEMENTS
REASONS a.
Given
<QPS = <TPR b.
<QPS = <QPR +<RPS
<TPR = <TPS + <RPS c. d.
Substitution e.
Subtraction f.
<QPS ≅ <TPR
Def. of congruent
Angle + Post.
<QPR +<RPS = <TPS +<RPS
<QPR= <TPS
<QPR≅ <TPS
Def. of Congruent