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

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

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

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

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

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

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

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

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

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

Key Concept

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

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

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

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

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

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

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

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

Concept

Concept

Use Corresponding Angles Postulate       Example 2

Use Corresponding Angles Postulate       Example 2

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

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

Concept

Concept

Use Theorems about Parallel Lines     Example 3

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

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 + 15 Substitution x – 10 = 15 Subtract x from each side. x = 25 Add 10 to each side. Answer: 25; Corresponding Angles Postulate Example 4

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

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

Concept