Identify the type of angles. 1. 5, 7 ANSWER corresponding 2. 3, 6 ANSWER alternate interior 3. 1, 8 ANSWER alternate exterior

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 4 and 8 are corresponding angles, by the Corresponding Angles Postulate, you know that m 8 = 120°.

Warm Up Identify the name of the angle pair ے4 and ے 8 ے 3 and ے 6 1 3 2 5 6 7 8

3.2 Using Parallel Lines & Transversals Patty Paper

Lesson 3.2 Postulates & Theorems

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.

If the Find:

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 4 = 115°. Lines a and b are parallel, so you can use the theorems about parallel lines. m 4 + (x+5)° = 180° Consecutive Interior Angles Theorem 115° + (x+5)° = 180° Substitute 115° for m 4. x + 120 = 180 Combine like terms. x = 60 Subtract 120 from each side.

GUIDED PRACTICE for Examples 1 and 2 Use the diagram. 1. If m 1 = 105°, find m 4, m 5, and m 8. Tell which postulate or theorem you use in each case. m 4 = 105° ANSWER Vertical Angles Congruence Theorem. m 5 = 105° Corresponding Angles Postulate. m 8 = 105° Alternate Exterior Angles Theorem

GUIDED PRACTICE for Examples 1 and 2 Use the diagram. 2. If m 3 = 68° and m 8 = (2x + 4)°, what is the value of x? Show your steps. m 7 + m 8 = 180 ANSWER m 3 = m 7 68 + 2x + 4 = 180 2x + 72 = 180 2x = 108 x = 54

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 2 = 40°. What is m 1? How do you know?

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, 1 2. By the definition of congruent angles, m 1 = m 2 = 40°.

What theorem justifies each statement? Daily Homework Quiz What theorem justifies each statement? 1. 3 6 Alt. Interior Thm. s ANSWER 2. 4 and 6 are supplementary. Consec. Interior Thm. s ANSWER 3. If m 2 = 115 , find m 7. o 115 ANSWER o

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

The figure shows a plant trellis . Daily Homework Quiz 5. The figure shows a plant trellis . If m 1 = 82o , find m 2. 82 ANSWER o