1. Parallel Lines & Transversals
Review:
1. Angles whose measures have a sum of 90° are _______________ .
2. Vertical angles have equal measures, so they are ______________.
3. Angles whose measures have a sum of 180° are ______________.
4. An angle that measures less than 90° is a(n) ____________ angle.
complementary
congruent
supplementary
acute

2. Parallel Lines & Transversals
Learn to identify parallel and perpendicular lines and the angles formed by a transversal.

3. Parallel Lines & Transversals
Vocabulary
parallel lines
transversal

4. Parallel Lines & Transversals
Parallel lines are lines in a plane that never meet, like a set of perfectly straight, infinite train tracks.
A transversal is a line that intersects two or more lines that lie in the same plane. Transversals to parallel lines form angles with special properties.

5. Parallel Lines & Transversals
The sides of the windows are transversals to the top and bottom.
The top and bottom of the windows are parallel.

6. Parallel Lines & Transversals
You cannot tell if angles are congruent by measuring because measurement is not exact.
Caution!

7. Parallel Lines & Transversals
Additional Example 1: Identifying Congruent Angles Formed by a Transversal
Measure the angles formed by the transversal and parallel lines. Which angles seem to be congruent?
1, 3, 5, and 7 all measure 150° and appear to be congruent.
 2, 4, 6, and 8 all measure 30° and appear to be congruent.

8. Additional Example 1 Continued
Angles circled in blue appear to be congruent to each other, and angles circled in red appear to be congruent to each other. 7 8

9. Check It Out: Example 1
Measure the angles formed by the transversal and parallel lines. Which angles seem to be congruent? 1 2 3 4 5 6 7 8
1, 4, 5, and 8 all measure 36° and appear to be congruent.
 2, 3, 6, and 7 all measure 144° and appear to be congruent.

10. Check It Out: Example 1 Continued
Angles marked in blue appear to be congruent to each other, and angles marked in red appear to be congruent to each other. 8 7 1 2 3 4 5 6 7 8

11. Some pairs of the eight angles formed by two parallel lines and a transversal have special names.

13. The symbol for parallel is ||. The symbol for perpendicular is .
Writing Math

14. Additional Example 2A: Finding Angle Measures of Parallel Lines Cut by Transversals
In the figure, line l || line m. Find the measure of the angle. 4
The 124 angle and 4 are corresponding angles.
m4 = 124°

15. Additional Example 2B: Finding Angle Measures of Parallel Lines Cut by Transversals Continued
In the figure, line l || line m. Find the measure of the angle. 2
2 is supplementary to angle 124°.
m ° = 180°
–124° –124°
m = 56°

16. Additional Example 2C: Finding Angle Measures of Parallel Lines Cut by Transversals Continued
In the figure, line l || line m. Find the measure of the angle. 6
6 is supplementary to angle 6.
m ° = 180°
–124° –124°
m = 56°
m6 = 56°

17. m7 = 144° Check It Out: Example 2A
In the figure, line n || line m. Find the measure of the angle. 7
The 144 angle and 7 are alternate exterior angles. 1
144° 3 4 5 6 7 8 m n
m7 = 144°

18. Check It Out: Example 2B
In the figure, line n || line m. Find the measure of the angle. 1
1 is supplementary to the 144° angle. 1
144° 3 4 5 6 7 8 m n
m ° = 180°
–144° –144°
m = 36°

19. m5 = 36° Check It Out: Example 2C
In the figure, line n || line m. Find the measure of the angle. 5
5 and 1 are corresponding angles. 1
144° 3 4 5 6 7 8 m n
m5 = 36°

20. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 20

21. Lesson Quiz
In the figure, a || b.
1. Name the angles congruent to 3.
1, 5, 7
2. Name all the angles supplementary to 6.
1, 3, 5, 7
3. If m1 = 105° what is m3?
105°
4. What is m6?
75°

22. Lesson Quiz for Student Response Systems
1. In the figure, x || y. Identify the angles congruent to 3.
A. 1, 2, 4
B. 2, 4, 6
C. 4, 5, 6
D. 1, 5, 8 22

23. Lesson Quiz for Student Response Systems
2. In the figure, x || y. If m5 = 115°, what is m7?
A. 25°
B. 65°
C. 75°
D. 115° 23