1. 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°.

2. 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.

3. 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.
ANSWER
m =
105°
Vertical Angles Congruence Theorem.
m =
105°
Corresponding Angles Postulate.
m =
105°
Alternate Exterior Angles Theorem

4. 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

5. EXAMPLE 3
Prove the Alternate Interior Angles Theorem
Prove that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
Draw a diagram. Label a pair of alternate interior angles as and You are looking for an angle that is related to both and Notice that one angle is a vertical angle with and a corresponding angle with Label it
SOLUTION

6. Prove the Alternate Interior Angles Theorem
EXAMPLE 3
Prove the Alternate Interior Angles Theorem
GIVEN :
p q
PROVE :
STATEMENTS
REASONS
p q 1. 1.
Given 2.
Corresponding Angles Postulate 2. 3. 3.
Vertical Angles Congruence Theorem 4.
Transitive Property of Congruence 4.

7. 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

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

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