Warm-Up Exercises

ANSWER alternate interior

1. 5, 7

2. 3, 6

3. 1, 8

ANSWER alternate exterior

ANSWER corresponding

Identify the type of angles.

Warm-Up ExercisesEXAMPLE 1 Identify congruent angles

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°.

The measure of three of the numbered angles is 120°. Identify the angles. Explain your reasoning.

Warm Up

Identify the name of the angle pair1) 4ے and 8 ے2) 3 ے and 6 ے3) 2 ے and 6ے4) 3ے and 7ے5) 5ے and 8ے6) 3ے and 4ے

43

1

5 67 8

2

3.2 Using Parallel Lines & Transversals

• Patty Paper

Lesson 3.2 Postulates & Theorems

3.2 Using Parallel Lines & Transversals

k

j

m

l

16 15 14 13

121110917

65

43

8

72

1

A. State the transversal that forms each pair of angles. B. Then identify the special angle name for each pair of

angles. 1. 1 and 5 _______________

2. 10 and 11 _____________

3. 8 and 6 _______________

4. 10 and 12 _____________

5. 2 and 6 _______________

6. 3 and 11 _______________

7. 2 and 16 ______________

8. 5 and 12 ______________

9. 7 and 9 _______________

10. 10 and 14 _____________

1 107 and 11 48m m

11. 3 _____ 12. 5 _____

13. 13 _____ 14. 9 _____

15. 15 _____ 16. 2 _____

17. 10 _____ 18. 17 _____

m m

m m

m m

m m

If the Find:

k

j

m

l

16 15 14 13

121110917

65

43

8

72

1

Warm-Up ExercisesEXAMPLE 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.

Consecutive Interior Angles Theoremm 4 + (x+5)° = 180°

Substitute 115° for m 4.115° + (x+5)° = 180°

Combine like terms.x + 120 = 180

Subtract 120 from each side.x = 60

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

Vertical Angles Congruence Theorem.

Corresponding Angles Postulate.m 5 =105°

Alternate Exterior Angles Theoremm 8 =105°

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

Warm-Up ExercisesGUIDED 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 3 = m 7

68 + 2x + 4 = 180

2x + 72 = 180

2x = 108

x = 54

m 7 + m 8 = 180ANSWER

Warm-Up ExercisesEXAMPLE 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?

Warm-Up ExercisesEXAMPLE 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°.

Warm-Up ExercisesDaily Homework Quiz

What theorem justifies each statement?

Alt. Interior Thm.sANSWER

2. 4 and 6 are supplementary.

Consec. Interior Thm.sANSWER

3. If m 2 = 115 , find m 7.o

115ANSWERo

1. 3 6

Warm-Up ExercisesDaily Homework Quiz

4. Find the values of x and y.

17.5, 35ANSWER

Warm-Up ExercisesDaily Homework Quiz

82ANSWERo

5. The figure shows a plant trellis .

If m 1 = 82o , find m 2.