1. 3.2 Parallel Lines and Transversals.
Geometry
3.2 Parallel Lines and Transversals.

2. Geometry 3.2 Parallel Lines and Transversals
Goals
Prove and use results about parallel lines and transversals.
Use properties about parallel lines to solve problems.
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

3. Theorem 3.1: Corr. Angles Theorem.
m || n n
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

4. This means ALL corresponding angles are congruent.1 2 3 4 5 6 7 8
1  5
2  6
3  7
4  8
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

5. Geometry 3.2 Parallel Lines and Transversals
Example
120° ?
60°
60° ?
120° ?
120° ?
60° ?
60° ? ?
120°
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

6. Theorem 3.2 Alt Int ’s Theorem
If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
2 lines ||  alt int s 
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

7. Theorem 3.3 Alt Exterior ’sTheorem
If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.
2 lines ||  alt ext s 
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

8. Theorem 3.4 Same side Int ’s Theorem
If two parallel lines are cut by a transversal, then same side interior angles are supplementary.
m1 + m2 = 180
m3 + m4 = 180 1 3 2 4
2 lines ||  ss int s supp
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

9. Geometry 3.2 Parallel Lines and Transversals
Theorems in a nutshell.
2 lines ||  corr s 
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

10. Geometry 3.2 Parallel Lines and Transversals
Theorems in a nutshell.
2 lines ||  alt. int. s 
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

11. Geometry 3.2 Parallel Lines and Transversals
Theorems in a nutshell.
2 lines ||  alt. ext. s 
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

12. Geometry 3.2 Parallel Lines and Transversals
Theorems in a nutshell.
2 lines ||  SS int. s supp.
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

13. Geometry 3.2 Parallel Lines and Transversals
These are the “reasons” for proof.
2 lines || 
corr s 
alt int s 
alt ext s 
ss int s supp
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

14. Geometry 3.2 Parallel Lines and Transversals
Sample problem 1 m n
m || n
(120 – x)°
Solve for x.
5x°
2 lines ||  alt ext s 
5x = 120 – x
6x = 120
x = 20
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

15. Geometry 3.2 Parallel Lines and Transversals
Sample problem 2 m n
m || n
Solve for x.
(x + 20)°
(x + 8)°
2 lines ||  SS int s supp
(x + 20) + (x + 8) = 180
2x + 28 = 180
2x = 152
x = 76
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

16. Geometry 3.2 Parallel Lines and Transversals
Sample problem 3 m n
m || n
Solve for x.
(x + 40)°
(x + 40)°
(x + 50)°
Linear Pair Post.
(x + 40) + (x + 50) = 180
2x + 90 = 180
2x = 90
x = 45
2 lines ||  corr s 
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

17. Geometry 3.2 Parallel Lines and Transversals
In Summary.
2 lines || 
corr s 
alt int s 
alt ext s 
ss int s supp
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

18. Geometry 3.2 Parallel Lines and Transversals
Extra for Experts m n
m || n x°
43°
25°
Find x.
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals

19. Geometry 3.2 Parallel Lines and Transversals
Solution m n
m || n x°
43°
25°
25°
43°
Find x.
x° = 25° + 43° = 68°
November 2, 2019
Geometry 3.2 Parallel Lines and Transversals