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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
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Make a conjecture about the next number in the sequence, 5, 20, 80, 320.
D. 1580 5-Minute Check 1
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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
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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
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A. Substitution Property B. Reflexive Property
Name the property that justifies the statement. If m1 + m2 = 75 and m2 = m3, then m1 + m3 = 75. A. Substitution Property B. Reflexive Property C. Addition Property D. Symmetric Property 5-Minute Check 4
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Find m1 and m2 if m1 = 8x + 18 and m2 = 16x – 6 and m1 and m2 are supplementary.
A. m1 = 106, m2 = 74 B. m1 = 74, m2 = 106 C. m1 = 56, m2 = 124 D. m1 = 14, m2 = 166 5-Minute Check 5
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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
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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
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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
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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
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Key Concept
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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
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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
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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
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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
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A. Classify the relationship between 4 and 5.
A. alternate interior B. alternate exterior C. corresponding D. consecutive interior Example 1a
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B. Classify the relationship between 7 and 9.
A. alternate interior B. alternate exterior C. corresponding D. consecutive interior Example 1b
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C. Classify the relationship between 4 and 7.
A. alternate interior B. alternate exterior C. corresponding D. consecutive interior Example 1c
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D. Classify the relationship between 2 and 11.
A. alternate interior B. alternate exterior C. corresponding D. consecutive interior Example 1d
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Concept
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Concept
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Use Corresponding Angles Postulate
Example 2
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Use Corresponding Angles Postulate
Example 2
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A. In the figure, a || b and m18 = 42. Find m22.
C. 48 D. 138 Example 2a
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B. In the figure, a || b and m18 = 42. Find m25.
C. 48 D. 138 Example 2b
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Concept
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Concept
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Use Theorems about Parallel Lines
Example 3
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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
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5 7 Corresponding Angles Postulate
Find Values of Variables ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. Explain your reasoning. 5 7 Corresponding Angles Postulate m5 = m7 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
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A. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find x.
A. x = 9 B. x = 12 C. x = 10 D. x = 14 Example 4a
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B. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find y.
A. y = 14 B. y = 20 C. y = 16 D. y = 24 Example 4b
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Concept
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