1. 3-2 Angles and Parallel Lines
You named angle pairs formed by parallel lines and transversals.
Use theorems to determine the relationships between specific pairs of angles.
Use algebra to find angle measurements.
Page 180

2. Parallel Crossing
You will need a sheet of paper, a straightedge and a protractor.
Draw two parallel lines.
Draw a transversal through the two lines.
Measure all the angles.
Do you see any patterns?

3. Postulate 3.1 p. 181
If parallel lines are cut by a transversal, then the Corresponding Angles are congruent.

4. Page 180

5. A. In the figure, m11 = 51. Find m15
A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used.
15  11 Corresponding Angles Postulate
m15 = m11 Definition of congruent angles
m15 = 51 Substitution
Answer: m15 = 51

6. B. In the figure, m11 = 51. Find m16
B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used.
16  15 Vertical Angles Theorem
15  11 Corresponding Angles Postulate
16  11 Transitive Property ()
m16 = m11 Definition of congruent angles
m16 = 51 Substitution
Answer: m16 = 51

7. A. In the figure, a || b and m18 = 42. Find m22.
C. 48
D. 138

8. A. In the figure, a || b and m18 = 42. Find m22.
C. 48
D. 138

9. Alternate Interior Angles Theorem
If parallel lines are cut by a transversal, then the Alternate Interior angles are congruent. x x x x

10. Page 181

11. FLOOR TILES The diagram represents the floor tiles in Michelle’s house
FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3.
2  3 Alternate Interior Angles Theorem
m2 = m3 Definition of congruent angles
125 = m3 Substitution
Answer: m3 = 125

12. FLOOR TILES The diagram represents the floor tiles in Michelle’s house
FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4.
A. 25
B. 55
C. 70
D. 125

13. A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
5  7 Corresponding Angles Postulate
m5 = m7 Definition of congruent angles
2x – 10 = x Substitution
x – 10 = 15 Subtract x from each side.
x = 25 Add 10 to each side.
Answer: x = 25

14. Theorems
If parallel lines are cut by a transversal, then Consecutive Interior angles are supplementary.

15. Theorems
If parallel lines are cut by a transversal, then the alternate exterior angles are congruent.

16. Page 181

17. What special relationships happen when a transversal crosses parallel lines?
If parallel lines are cut by a transversal, then the alternate interior angles are congruent.
If parallel lines are cut by a transversal, then the corresponding angles are congruent.
If parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
If parallel lines are cut by a transversal, then same-side interior angles are supplementary.

18. This is a special relationship that exists when the transversal of two parallel lines is a perpendicular line.
Page 182

19. 3-2 Assignment
p. 183, 11-19, 24-28