1. Angles Formed by Transversals
Lesson 3.3

2. Objectives
Identify angles formed by transversals.

3. Key Vocabulary Transversal Interior angles Exterior angles
Corresponding angles
Alternate interior angles
Alternate exterior angles
Same-side interior angles

4. Transversal
Transversal - a line that intersects two or more coplanar lines at different points.
Line ℓ is a transversal of lines q and r.
Line ℓ forms a total of eight angles with lines q and r. These angles, and specific pairings of these angles, are given special names. 2 4 7 1 3 5 6 8
Two coplanar lines
Transversal ℓ q r

5. Transversal
Lines intersected by a transversal can be parallel or not parallel.

6. Transversal Angle Pair Relationships2 4 7 1 3 5 6 8 ℓ q r
exterior
interior
Interior angles (4 ∠’s) lie in the region between lines q and r. (∠3, ∠4, ∠5, ∠6)
Exterior angles (4 ∠’s) lie in the two regions that are not between lines q and r, the regions above line q and below line r. (∠1, ∠2, ∠7, ∠8)

7. Transversal Angle Pair Relationships2 4 7 1 3 5 6 8 ℓ q r
exterior
interior
Same-side interior angles – pair of interior angles that lie on the same side of transversal ℓ. (∠3 & ∠5, ∠4 & ∠6)
Alternate interior angles – pair of nonadjacent interior angles that lie on opposite sides of transversal ℓ. (∠3 & ∠6, ∠4 & ∠5)

8. Transversal Angle Pair Relationships2 4 7 1 3 5 6 8 ℓ q r
exterior
interior
Alternate exterior angles – pair of nonadjacent exterior angles that lie on opposite sides of transversal ℓ. (∠1 & ∠8, ∠2 & ∠7)
Corresponding angles – pair of angles that lie on the same side of transversal ℓ and on the same side of lines q and r. (∠1 & ∠5, ∠2 & ∠6, ∠3 & ∠7, ∠4 & ∠8)

9. Check For Understanding

10. Pairs Of Angles Formed by a Transversal
A line that intersects two or more lines at different points is called a transversal. G F
Line L (transversal)
Line M B A P
Line N D C Q
Four angles are formed at point P and another four at point Q by the transversal L.
Line M and line N are parallel lines.
Line L intersects line M and line N at point P and Q.
Eight angles are formed in all by the transversal L.

11. Corresponding Angles
A transversal creates two groups of four angles in each group. Corresponding angles are two angles, one in each group, in the same relative position. 1 2 m 3 4 5 6 n 7 8

12. Alternate Interior Angles
When a transversal cuts two lines, alternate interior angles are angles within the two lines on alternate sides of the transversal. m 1 3 4 2 n

13. Alternate Exterior Angles
When a transversal cuts two lines, alternate exterior angles are angles outside of the two lines on alternate sides of the transversal. 1 3 m n 4 2

14. Same-Side Interior Angles
When a transversal cuts two lines, interior angles on the same side of the transversal are angles within the two lines on the same side of the transversal. m 1 3 2 4 n

15. Name the pairs of the following angles formed by a transversal.
Line M B A
Line N D E P Q G F
Line L
Line M B A
Line N D E P Q G F
Line L
Line M B A
Line N D E P Q G F
Line L
Test Yourself
Corresponding angles
Alternate interior angles
Same-side interior angles

16. Parallel Lines and Transversals
Determine if the statement is true or false. If false, correct the statement.
1. Line r is a transversal of lines p and q. True – Line r intersects both lines in a plane. 2. ∠2 and ∠6 are alternate interior angles. False - The angles are corresponding angles on transversal p. r 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s p q

17. Parallel Lines and Transversals
Determine if the statement is true or false. If false, correct the statement.
3. ∠9 and ∠11 are alternate interior angles. False – The angles are vertical angles created by the intersection of q and r. 4. ∠1 and ∠7 are alternate exterior angles. True - The angles are alternate exterior angles on transversal p. r 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s p q

18. Parallel Lines and Transversals
Determine if the statement is true or false. If false, correct the statement.
5. ∠12 and ∠14 are alternate interior angles. True – The angles are alternate interior angles on transversal q. 6. ∠6 and ∠13 are same-side interior angles. True – The angles are same-side interior angles on transversal s. r 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s p q

19. Parallel Lines and Transversals
Determine if the statement is true or false. If false, correct the statement.
7. ∠9 and ∠10 are alternate exterior angles. False – The angles are a linear pair with linear rays on line r. 8. ∠8 and ∠16 are corresponding angles. True – The angles are corresponding on transversal s. r 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s p q

20. Example 1 Describe the relationship between the angles. a. 1 and 2
SOLUTION
alternate interior angles a.
alternate exterior angles b.
same-side interior angles c. 20

21. Example 2 List all pairs of angles that fit the description.
a. corresponding
b. alternate exterior
c. alternate interior
d. same-side interior
SOLUTION
corresponding a.
1 and 5
2 and 6
3 and 7
4 and 8 21

22. Example 2 alternate exterior: b. 1 and 8 3 and 6
alternate interior: c.
2 and 7
4 and 5
same-side interior: d.
2 and 5
4 and 7 22

23. Your Turn: Describe the relationship between the angles. 2 and 7 1.
ANSWER
alternate exterior angles
3 and 5 2.
ANSWER
same-side interior angles
1 and 5 3.
ANSWER
corresponding angles

24. 4 and 5 4.
ANSWER
alternate interior angles
4 and 8 5.
ANSWER
corresponding angles
4 and 6 6.
ANSWER
same-side interior angles

25. Example 3a:
Identify ∠7 and ∠3 as alternate interior, alternate exterior, corresponding, or same-side interior angles.
Answer: corresponding

26. Example 3b:
Identify ∠8 and ∠2 as alternate interior, alternate exterior, corresponding, or same-side interior angles.
Answer: alternate exterior

27. Example 3c:
Identify ∠5 and ∠1 as alternate interior, alternate exterior, corresponding, or same-side interior angles.
Answer: corresponding

28. Example 3d:
Identify ∠7 and ∠1 as alternate interior, alternate exterior, corresponding, or same-side interior angles.
Answer: alternate exterior

29. Example 3e:
Identify ∠3 and ∠9 as alternate interior, alternate exterior, corresponding, or same-side interior angles.
Answer: alternate interior

30. Example 3f:
Identify ∠7 and ∠10 as alternate interior, alternate exterior, corresponding, or same-side interior angles.
Answer: same-side interior

31. Your Turn:
Identify each pair of angles as alternate interior, alternate exterior, corresponding, or same-side interior angles. a. b. c.
Answer: same-side interior
Answer: corresponding
Answer: alternate exterior

32. Your Turn:
Identify each pair of angles as alternate interior, alternate exterior, corresponding, or same-side interior angles. d. e. f.
Answer: alternate interior
Answer: corresponding
Answer: alternate exterior

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

34. Example 4: Identifying Angle Pairs and Transversals
Identify the transversal and classify each angle pair.
A. 1 and 3
transversal l
corr. s
B. 2 and 6
transversal n
alt. int s
C. 4 and 6
transversal m
alt. ext s

35. Your Turn
Identify the transversal and classify the angle pair 2 and 5 in the diagram.
transversal n
consecutive int. s.

36. Joke Time What has 18 legs and catches flies? A baseball team.
Who stole the soap?
The robber ducky!
What happened to the plant on the windowsill of the classroom?
It grew square roots!

37. Assignment
Section 3.3, pg : #1-8 all, 9-41 odd