1. Splash Screen

2. Five-Minute Check (over Lesson 3–1) CCSS Then/Now
Postulate 3.1: Corresponding Angles Postulate
Example 1: Use Corresponding Angles Postulate
Theorems: Parallel Lines and Angle Pairs
Proof: Alternate Interior Angles Theorem
Example 2: Real-World Example: Use Theorems about Parallel Lines
Example 3: Find Values of Variables
Theorem 3.4: Perpendicular Transversal Theorem
Lesson Menu

3. Choose the plane parallel to plane MNR.
A. RST
B. PON
C. STQ
D. POS
5-Minute Check 1

4. Choose the plane parallel to plane MNR.
A. RST
B. PON
C. STQ
D. POS
5-Minute Check 1

5. Choose the segment skew to MP.
A. PM
B. TS
C. PO
D. MQ
___
5-Minute Check 2

6. Choose the segment skew to MP.
A. PM
B. TS
C. PO
D. MQ
___
5-Minute Check 2

7. Classify the relationship between 1 and 5.
A. corresponding angles
B. vertical angles
C. consecutive interior angles
D. alternate exterior angles
5-Minute Check 3

8. Classify the relationship between 1 and 5.
A. corresponding angles
B. vertical angles
C. consecutive interior angles
D. alternate exterior angles
5-Minute Check 3

9. Classify the relationship between 3 and 8.
A. alternate interior angles
B. alternate exterior angles
C. corresponding angles
D. consecutive interior angles
5-Minute Check 4

10. Classify the relationship between 3 and 8.
A. alternate interior angles
B. alternate exterior angles
C. corresponding angles
D. consecutive interior angles
5-Minute Check 4

11. Classify the relationship between 4 and 6.
A. alternate interior angles
B. alternate exterior angles
C. corresponding angles
D. vertical angles
5-Minute Check 5

12. Classify the relationship between 4 and 6.
A. alternate interior angles
B. alternate exterior angles
C. corresponding angles
D. vertical angles
5-Minute Check 5

13. Which of the following segments is not parallel to PT?
A. OS
B. TS
C. NR
D. MQ
5-Minute Check 6

14. Which of the following segments is not parallel to PT?
A. OS
B. TS
C. NR
D. MQ
5-Minute Check 6

15. G.CO.9 Prove theorems about lines and angles. Mathematical Practices
Content Standards
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.CO.9 Prove theorems about lines and angles.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
CCSS

16. You named angle pairs formed by parallel lines and transversals.
Use theorems to determine the relationships between specific pairs of angles.
Use algebra to find angle measurements.
Then/Now

17. Concept

18. 15  11 Corresponding Angles Postulate
Use Corresponding Angles Postulate
A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used.
15  11 Corresponding Angles Postulate
m15 = m11 Definition of congruent angles
m15 = 51 Substitution
Answer:
Example 1

19. 15  11 Corresponding Angles Postulate
Use Corresponding Angles Postulate
A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used.
15  11 Corresponding Angles Postulate
m15 = m11 Definition of congruent angles
m15 = 51 Substitution
Answer: m15 = 51
Example 1

20. 16  15 Vertical Angles Theorem
Use Corresponding Angles Postulate
B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used.
16  15 Vertical Angles Theorem
15  11 Corresponding Angles Postulate
16  11 Transitive Property ()
m16 = m11 Definition of congruent angles
m16 = 51 Substitution
Answer:
Example 1

21. 16  15 Vertical Angles Theorem
Use Corresponding Angles Postulate
B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used.
16  15 Vertical Angles Theorem
15  11 Corresponding Angles Postulate
16  11 Transitive Property ()
m16 = m11 Definition of congruent angles
m16 = 51 Substitution
Answer: m16 = 51
Example 1

22. A. In the figure, a || b and m18 = 42. Find m22.
C. 48
D. 138
Example 1a

23. A. In the figure, a || b and m18 = 42. Find m22.
C. 48
D. 138
Example 1a

24. B. In the figure, a || b and m18 = 42. Find m25.
C. 48
D. 138
Example 1b

25. B. In the figure, a || b and m18 = 42. Find m25.
C. 48
D. 138
Example 1b

26. Concept

27. Concept

28. 2  3 Alternate Interior Angles Theorem
Use Theorems about Parallel Lines
FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3.
2  3 Alternate Interior Angles Theorem
m2 = m3 Definition of congruent angles
125 = m3 Substitution
Answer:
Example 2

29. 2  3 Alternate Interior Angles Theorem
Use Theorems about Parallel Lines
FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3.
2  3 Alternate Interior Angles Theorem
m2 = m3 Definition of congruent angles
125 = m3 Substitution
Answer: m3 = 125
Example 2

30. FLOOR TILES The diagram represents the floor tiles in Michelle’s house
FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4.
A. 25
B. 55
C. 70
D. 125
Example 2

31. FLOOR TILES The diagram represents the floor tiles in Michelle’s house
FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4.
A. 25
B. 55
C. 70
D. 125
Example 2

32. A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
Find Values of Variables
A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
5  7 Corresponding Angles Postulate
m5 = m7 Definition of congruent angles
2x – 10 = x Substitution
x – 10 = 15 Subtract x from each side.
x = 25 Add 10 to each side.
Answer:
Example 3

33. A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
Find Values of Variables
A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
5  7 Corresponding Angles Postulate
m5 = m7 Definition of congruent angles
2x – 10 = x Substitution
x – 10 = 15 Subtract x from each side.
x = 25 Add 10 to each side.
Answer: x = 25
Example 3

34. B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.
Find Values of Variables
B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.
8  6 Corresponding Angles Postulate
m8 = m6 Definition of congruent angles
4y = m6 Substitution
Example 3

35. m6 + m4 = 180 Supplement Theorem 4y + 4(y – 25) = 180 Substitution
Find Values of Variables
m6 + m4 = 180 Supplement Theorem
4y + 4(y – 25) = 180 Substitution
4y + 4y – 100 = 180 Distributive Property
8y = 280 Add 100 to each side.
y = 35 Divide each side by 8.
Answer:
Example 3

36. m6 + m4 = 180 Supplement Theorem 4y + 4(y – 25) = 180 Substitution
Find Values of Variables
m6 + m4 = 180 Supplement Theorem
4y + 4(y – 25) = 180 Substitution
4y + 4y – 100 = 180 Distributive Property
8y = 280 Add 100 to each side.
y = 35 Divide each side by 8.
Answer: y = 35
Example 3

37. A. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find x.
A. x = 9
B. x = 12
C. x = 10
D. x = 14
Example 3

38. A. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find x.
A. x = 9
B. x = 12
C. x = 10
D. x = 14
Example 3

39. B. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find y.
A. y = 14
B. y = 20
C. y = 16
D. y = 24
Example 3

40. B. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find y.
A. y = 14
B. y = 20
C. y = 16
D. y = 24
Example 3

41. Concept

42. End of the Lesson