Warm-Up Exercises ANSWER alternate interior 1. 5, 7 . 3, 6 . 1, 8 ANSWER alternate exterior ANSWER corresponding Identify the type of angles.
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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.
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