1. 3-3: Proving Lines Parallel
Do NOW
2/18/ :31 PM
3-3: Proving Lines Parallel

2. Page 158 (Answers may vary)7)
100° 9)
102°
11)
90°
13)
120°, Correspond. Angle Post.
15)
60°, Same-Side Int. Angle Thrm.
17)
60°, Linear Pair Theorem
19)
120°, Vertical Angle Theorem
21)
x = 4, Same Side Int. Angle Thrm.
Angle 3: 103°, Angle 4: 77°
23)
x = 3, Corr. Angle Post.
Angle 1 = Angle 4 = 42°
27)
28)
Impossible, Same-Side interior angles are supplementary, not complementary
31)
Choice A is incorrect because angles are supplementary and not congruent
37)
75°
2/18/ :31 PM
3-3: Proving Lines Parallel

3. 3-3: Proving Lines Parallel
2/18/ :31 PM
3-3: Proving Lines Parallel

4. Angles with Parallel Line Systems
Section 3-3A
Geometry PreAP, Revised ©2013
2/18/ :31 PM
3-3: Proving Lines Parallel

5. 3-3: Proving Lines Parallel
Example 1
Find the value of x in each question given that lines l and m are parallel. Check your answers by finding the measure of each angle given that 𝒎∠𝑪=𝟑𝒙−𝟏𝟎 and 𝒎∠𝑭=𝒙+𝟕𝟎
2/18/ :31 PM
3-3: Proving Lines Parallel

6. 3-3: Proving Lines Parallel
Example 2
Find the value of x in each question given that lines l and m are parallel. Check your answers by finding the measure of each angle given that 𝒎∠𝑩=𝟐 𝒙+𝟒𝟎 and 𝒎∠𝑮=𝟓𝒙+𝟒𝟒
2/18/ :31 PM
3-3: Proving Lines Parallel

7. 3-3: Proving Lines Parallel
Your Turn
Find the value of x in each question given that lines l and m are parallel. Check your answers by finding the measure of each angle given that 𝒎∠𝑫=𝒙+𝟐𝟕 and 𝒎∠𝑭=𝟐𝒙−𝟑𝟗
2/18/ :31 PM
3-3: Proving Lines Parallel

8. 3-3: Proving Lines Parallel
Example 3
Given 𝒍∥𝒎, find the value (s) of x and each angle. Check for extraneous solutions. Given: 𝒎∠𝟑= 𝒙 𝟐 +𝟏𝟏𝟐 and 𝒎∠𝟖=𝟏𝟔𝒙+𝟏𝟑𝟏
2/18/ :31 PM
3-3: Proving Lines Parallel

9. 3-3: Proving Lines Parallel
Example 4
Given 𝒍∥𝒎, find the value (s) of x and each angle. Check for extraneous solutions. Given: 𝒎∠𝟑= 𝒙 𝟐 −𝟐𝒙 and 𝒎∠𝟔=𝟑𝒙+𝟏𝟎𝟖
2/18/ :31 PM
3-3: Proving Lines Parallel

10. 3-3: Proving Lines Parallel
Your Turn
Given 𝒍∥𝒎, find the value (s) of x and each angle. Check for extraneous solutions. Given: 𝒎∠𝟏= 𝒙 𝟐 −𝟕𝒙 and 𝒎∠𝟕=−𝒙+𝟕
2/18/ :31 PM
3-3: Proving Lines Parallel

11. 3-3: Proving Lines Parallel
Example 5
Given 𝒑∥𝒕, find the value (s) of x and each angle. Check for extraneous solutions. Given: 𝒎∠𝟏=𝟏𝟐𝒙−𝟒𝒚, 𝒎∠𝟖=𝒙−𝟒𝒚, and 𝒎∠𝟓=𝟏𝟓𝒙+𝟖𝒚
2/18/ :31 PM
3-3: Proving Lines Parallel

12. 3-3: Proving Lines Parallel
Example 6
Given 𝒑∥𝒕, find the value (s) of x and each angle. Check for extraneous solutions. Given: 𝒎∠𝟐=𝟖𝒃+𝒂, 𝒎∠𝟓=𝟕𝒂+𝟐𝟓𝒃, and 𝒎∠𝟒=𝟑𝒂+𝟓𝒃
2/18/ :31 PM
3-3: Proving Lines Parallel

13. 3-3: Proving Lines Parallel
Your Turn
Given 𝒑∥𝒕, find the value (s) of x and each angle. Check for extraneous solutions. Given: 𝒎∠𝟑=𝟏𝟒𝒔−𝟑𝒕, 𝒎∠𝟕=𝟗𝒔+𝟏𝟐𝒕, and 𝒎∠𝟒=𝟓𝒔+𝟔𝒕
2/18/ :31 PM
3-3: Proving Lines Parallel

14. 3-3: Proving Lines Parallel
Example 7
Given 𝒍∥𝒎. Prove: ∠𝟏 & ∠𝟐 are supplementary
Statement
Reason
1) 𝒍∥𝒎
Given
2) ∠𝟏≅∠𝟑
Linear Pair Theorem
3) m∠𝟏=𝑚∠𝟑
Def’n of Congruency
4) ∠𝟑 & ∠𝟐 are supplementary
Same Side Interior Angle Theorem
5) m∠𝟑+𝑚∠𝟐=𝟏𝟖𝟎°
Def’n of Supplementary
6) m∠𝟏+𝑚∠𝟐=𝟏𝟖𝟎°
Substitution
7) ∠𝟏 & ∠𝟐 are supplementary
2/18/ :31 PM
3-3: Proving Lines Parallel