1. Five-Minute Check (over Lesson 2–6) Mathematical Practices Then/Now
New Vocabulary
Example 1: Classify Angle Pair Relationships
Theorems: Parallel Lines and Angle Pairs
Postulate 2.12: Corresponding Angles Postulate
Example 2: Use Corresponding Angles Postulate
Proof: Alternate Interior Angles Theorem
Example 3: Real-World Example: Use Theorems about Parallel Lines
Example 4: Find Values of Variables
Theorem 2.17: Perpendicular Transversal Theorem
Lesson Menu

2. Make a conjecture about the next number in the sequence, 5, 20, 80, 320.
D. 1580
5-Minute Check 1

3. B. If you live in Massachusetts, then you do not live in Boston.
Write the contrapositive of this statement. If you live in Boston, then you live in Massachusetts.
A. If you do not live in Massachusetts, then you do not live in Boston.
B. If you live in Massachusetts, then you do not live in Boston.
C. If you do not live in Massachusetts, then you live in Boston.
D. You might live in Massachusetts or Boston.
5-Minute Check 2

4. A. Yes, A and B are a linear pair. B. no conclusion
Use the Law of Detachment or the Law of Syllogism to determine whether a valid conclusion can be reached from the following set of statements. If two angles form a linear pair and are congruent, they are both right angles. A and B are both right angles.
A. Yes, A and B are a linear pair.
B. no conclusion
5-Minute Check 3

5. A. Substitution Property B. Reflexive Property
Name the property that justifies the statement. If m1 + m2 = 75 and m2 = m3, then m1 + m3 = 75.
A. Substitution Property
B. Reflexive Property
C. Addition Property
D. Symmetric Property
5-Minute Check 4

6. Find m1 and m2 if m1 = 8x + 18 and m2 = 16x – 6 and m1 and m2 are supplementary.
A. m1 = 106, m2 = 74
B. m1 = 74, m2 = 106
C. m1 = 56, m2 = 124
D. m1 = 14, m2 = 166
5-Minute Check 5

7. The measures of two complementary angles are x + 54 and 2x
The measures of two complementary angles are x + 54 and 2x. What is the measure of the smaller angle?
A. 24
B. 42
C. 68
D. 84
5-Minute Check 6

8. Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
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. MP

9. You used angle and line segment relationships to prove theorems.
Name angle pairs formed by lines and transversals.
Use theorems to determine the relationships between specific pairs of angles.
Then/Now

10. consecutive interior angles alternate interior angles
transversal
interior angles
exterior angles
consecutive interior angles
alternate interior angles
alternate exterior angles
corresponding angles
parallel lines
Vocabulary

11. Key Concept

12. Answer: corresponding
Classify Angle Pair Relationships
A. Classify the relationship between 2 and 6 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: corresponding
Example 1a

13. Answer: alternate exterior
Classify Angle Pair Relationships
B. Classify the relationship between 1 and 7 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: alternate exterior
Example 1b

14. Answer: consecutive interior
Classify Angle Pair Relationships
C. Classify the relationship between 3 and 8 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: consecutive interior
Example 1c

15. Answer: alternate interior
Classify Angle Pair Relationships
D. Classify the relationship between 3 and 5 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: alternate interior
Example 1d

16. A. Classify the relationship between 4 and 5.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
Example 1a

17. B. Classify the relationship between 7 and 9.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
Example 1b

18. C. Classify the relationship between 4 and 7.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
Example 1c

19. D. Classify the relationship between 2 and 11.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
Example 1d

20. Concept

21. Concept

22. Use Corresponding Angles Postulate
Example 2

23. Use Corresponding Angles Postulate
Example 2

24. A. In the figure, a || b and m18 = 42. Find m22.
C. 48
D. 138
Example 2a

25. B. In the figure, a || b and m18 = 42. Find m25.
C. 48
D. 138
Example 2b

26. Concept

27. Concept

28. Use Theorems about Parallel Lines
Example 3

29. 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 3

30. 5  7 Corresponding Angles Postulate
Find Values of Variables
ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. Explain your reasoning.
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: 25; Corresponding Angles Postulate
Example 4

31. 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 4a

32. 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 4b

33. Concept