Transcript 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)
 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 + 3x+18 = 180
<2 = 3x+18 4x+28=180
4x=152
X=38
Supplement Theorem
2. <4 = 2x-5
<5 = 4x-13
<3 = 90
<4 = 2(18)-5 = 31
<5 = 4(18)-13 = 59
<1 = x+10 = 38+10 = 48
<2 = 3(38)+18 = 132
2x-5+4x-13 = 90
6x-18 = 90
6x=108
X=18
Complement Theorem
Practice
1. <6 = 7x-24 7x-24 = 5x+14
<7 = 5x+14 2x = 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 supplementary
REASONS
given
<1& <2 are supplementary Def. of linear pair
<1 + < 2 = 180
Def. of supplementary
Def. of supplementary
<2+<3 = 180
<1+<2=<2+<3
Substitution
<1 = <3
Subtraction
<1 ≅ <3
Def. of Congruence
Practice – Fill in the proof
STATEMENTS
REASONS
a. <QPS ≅ <TPR
Given
<QPS = <TPR
b. Def. of congruent
<QPS = <QPR +<RPS
c. Angle + Post.
<TPR = <TPS + <RPS
d. <QPR +<RPS = <TPS +<RPS Substitution
e. <QPR= <TPS
f. <QPR≅ <TPS
Subtraction
Def. of Congruent