1. Objectives Identify parallel, perpendicular, and skew lines.
Identify the angles formed by two lines and a transversal.

2. Vocabulary parallel lines perpendicular lines skew lines
parallel planes
transversal
corresponding angles
alternate interior angles
alternate exterior angles
same-side interior angles

3. D

4. Segments or rays are parallel, perpendicular, or skew if the lines that contain them are parallel, perpendicular, or skew.
Helpful Hint

5. Example 1: Identifying Types of Lines and Planes
Identify each of the following.
A. a pair of parallel segments
B. a pair of skew segments
C. a pair of perpendicular segments
D. a pair of parallel planes

6. Check It Out! Example 1
Identify each of the following.
a. a pair of parallel segments
b. a pair of skew segments
c. a pair of perpendicular segments
d. a pair of parallel planes

8. Example 2: Classifying Pairs of Angles
Give an example of each angle pair.
A. corresponding angles
B. alternate interior angles
C. alternate exterior angles
D. same-side interior angles

9. Check It Out! Example 2
Give an example of each angle pair.
A. corresponding angles
B. alternate interior angles
C. alternate exterior angles
D. same-side interior angles

10. To determine which line is the transversal for a given angle pair, locate the line that connects the vertices.
Helpful Hint

11. Example 3: Identifying Angle Pairs and Transversals
Identify the transversal and classify each angle pair.
A. 1 and 3
B. 2 and 6
C. 4 and 6

12. Check It Out! Example 3
Identify the transversal and classify the angle pair 2 and 5 in the diagram.

13. Assignment
Pg 149 #14-17, 26-32

15. Example 1: Using the Corresponding Angles Postulate
Find each angle measure.
A. mECF
B. mDCE

16. Check It Out! Example 1
Find mQRS.

17. If a transversal is perpendicular to two parallel lines, all eight angles are congruent.
Helpful Hint

18. Example 2: Finding Angle Measures
Find each angle measure.
A. mEDG
B. mBDG

19. Check It Out! Example 2
Find mABD.

20. Example 3: Music Application
Find x and y in the diagram.

21. Check It Out! Example 3
Find the measures of the acute angles in the diagram.

22. Assignment
Pg 158 #6-25, 31

23. Objective
Use the angles formed by a transversal to prove two lines are parallel.

24. Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.

26. Example 1A: Using the Converse of the Corresponding Angles Postulate
Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.
4  8

27. Example 1B: Using the Converse of the Corresponding Angles Postulate
Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.
m3 = (4x – 80)°,
m7 = (3x – 50)°, x = 30

28. Check It Out! Example 1a
Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.
m1 = m3

29. Check It Out! Example 1b
Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.
m7 = (4x + 25)°,
m5 = (5x + 12)°, x = 13

30. The Converse of the Corresponding Angles Postulate is used to construct parallel lines. The Parallel Postulate guarantees that for any line ℓ, you can always construct a parallel line through a point that is not on ℓ.

32. Example 2A: Determining Whether Lines are Parallel
Use the given information and the theorems you have learned to show that r || s.
4  8

33. Example 2B: Determining Whether Lines are Parallel
Use the given information and the theorems you have learned to show that r || s.
m2 = (10x + 8)°,
m3 = (25x – 3)°, x = 5

34. Example 2B Continued
Use the given information and the theorems you have learned to show that r || s.
m2 = (10x + 8)°,
m3 = (25x – 3)°, x = 5

35. Check It Out! Example 2a
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
m4 = m8

36. Check It Out! Example 2b
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
m3 = 2x, m7 = (x + 50), x = 50

37. Example 3: Proving Lines Parallel
Given: p || r , 1  3
Prove: ℓ || m

38. Example 3 Continued
Statements
Reasons
1. p || r
2. 3  2
3. 1  3
4. Trans. Prop. of 

39. Check It Out! Example 3
Given: 1  4, 3 and 4 are supplementary.
Prove: ℓ || m

40. Check It Out! Example 3 Continued
Statements
Reasons
1. 1  4
2. m1 = m4
3. Given
4. m3 + m4 = 180
4. Trans. Prop. of 
5. m3 + m1 = 180
6. m2 = m3
7. Substitution
8. ℓ || m

41. Example 4: Carpentry Application
A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m1= (8x + 20)° and m2 = (2x + 10)°. If x = 15, show that pieces A and B are parallel.

42. Example 4 Continued
The same-side interior angles are supplementary, so pieces A and B are parallel by the Converse of the Same-Side Interior Angles Theorem.

43. Assignment
Pg 166 #1-11, 30-35

44. Vocabulary
perpendicular bisector
distance from a point to a line

45. The _________________of a segment is a line perpendicular to a segment at the segment’s midpoint.
The shortest segment from a point to a line is perpendicular to the line. This fact is used to define the ________________________ as the length of the perpendicular segment from the point to the line.

46. Example 1: Distance From a Point to a Line
A. Name the shortest segment from point A to BC.
B. Write and solve an inequality for x.

47. Check It Out! Example 1
A. Name the shortest segment from point A to BC.
B. Write and solve an inequality for x.

48. HYPOTHESIS
CONCLUSION

49. Example 3: Carpentry Application
A carpenter’s square forms a
right angle. A carpenter places
the square so that one side is
parallel to an edge of a board, and then draws a line along the other side of the square. Then he slides the square to the right and draws a second line. Why must the two lines be parallel?