1. Identify the type of angles.
, 7
ANSWER
corresponding
, 6
ANSWER
alternate interior
, 8
ANSWER
alternate exterior

2. EXAMPLE 1
Identify congruent angles
The measure of three of the numbered angles is 120°. Identify the angles. Explain your reasoning.
SOLUTION
By the Corresponding Angles Postulate, m 5 = 120°. Using the Vertical Angles Congruence Theorem, m 4 = 120°. Because and are corresponding angles, by the Corresponding Angles Postulate, you know that m = 120°.

3. Warm Up Identify the name of the angle pair ے4 and ے 8 ے 3 and ے 61 3 2 5 6 7 8

4. 3.2 Using Parallel Lines & Transversals
Patty Paper

5. Lesson 3.2 Postulates & Theorems

7. 3.2 Using Parallel Lines & Transversals
State the transversal that forms each pair of angles.
B. Then identify the special angle name for each pair of angles.

8. If the
Find:

9. Use properties of parallel lines
EXAMPLE 2
Use properties of parallel lines
ALGEBRA
Find the value of x.
SOLUTION
By the Vertical Angles Congruence Theorem, m = 115°. Lines a and b are parallel, so you can use the theorems about parallel lines.
m (x+5)° =
180°
Consecutive Interior Angles Theorem
115° + (x+5)° =
180°
Substitute 115° for m
x =
180
Combine like terms.
x = 60
Subtract 120 from each side.

10. GUIDED PRACTICE for Examples 1 and 2 Use the diagram. 1.
If m = 105°, find m 4, m 5, and m Tell which postulate or theorem you use in each case.
m =
105°
ANSWER
Vertical Angles Congruence Theorem.
m =
105°
Corresponding Angles Postulate.
m =
105°
Alternate Exterior Angles Theorem

11. GUIDED PRACTICE
for Examples 1 and 2
Use the diagram. 2.
If m = 68° and m = (2x + 4)°, what is the value of x? Show your steps.
m m =
180
ANSWER
m =
m 7
68 + 2x + 4 =
180
2x + 72 =
180
2x =
108
x = 54

12. EXAMPLE 4
Solve a real-world problem
Science
When sunlight enters a drop of rain, different colors of light leave the drop at different angles. This process is what makes a rainbow. For violet light, m = 40°. What is m 1? How do you know?

13. EXAMPLE 4
Solve a real-world problem
SOLUTION
Because the sun’s rays are parallel, 1 and 2 are alternate interior angles. By the Alternate Interior Angles Theorem, By the definition of congruent angles, m = m = 40°.

14. What theorem justifies each statement?
Daily Homework Quiz
What theorem justifies each statement? 1.
Alt. Interior Thm. s
ANSWER 2.
4 and are supplementary.
Consec. Interior Thm. s
ANSWER 3.
If m = 115 , find m o
115
ANSWER o

15. Daily Homework Quiz 4.
Find the values of x and y.
17.5, 35
ANSWER

16. The figure shows a plant trellis .
Daily Homework Quiz 5.
The figure shows a plant trellis .
If m = 82o , find m 82
ANSWER o