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Geometry I've got a theory that if you give 100 percent all of the time, somehow things will work out in the end. Larry Bird Today: •Homework Check •3.5 Instruction •Multiple Choice Practice •Practice Yesterday I've got a theory that if you give 100 percent all of the time, somehow things will work out in the end. Larry Bird •Recognize angle pairs that occur with parallel lines. • Prove that two lines are parallel from the angle pairs. Content Standards G.CO.9 Prove theorems about lines and angles. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 3.5 Proving Lines Parallel Objectives: 1. Prove lines are parallel Vocabulary: parallel, transversal, corresponding, alternate interior, alternate exterior, consecutive interior 3.2 Review If 2 parallel lines are cut by a transversal, then: corresponding angles are congruent. alternate interior angles are congruent. alternate exterior angles are congruent. consecutive interior angles are supplementary. 1 2 4 3 5 6 8 7 3.5 Proving Lines Parallel The converse is also true: If: corresponding angles are congruent, alternate interior angles are congruent, alternate exterior angles are congruent, consecutive interior angles are supplementary, then the lines are parallel. Determine which lines, if any, are parallel. Explain why!!!! Answer: Not b and c, because 77 + 100 is not 180 and consecutive interior are supposed to be supplementary. Can move 77 with vertical, so 103 + 77 = 180. Your Turn: Pair-Share Determine which lines, if any, are parallel. EXPLAIN! Answer: Statements Reasons 1. Given ALWAYS 2. Vertical Angles Are Congruent. 3. Transitive Property of Congruency. 4. Substitution Property of Congruency. 5. If Alternate Interior Angles Are Cong, Then Lines Are Parallel. Which lines if any are parallel? WHY? l1 l2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 l4 l3 Over Chapter 2 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 Over Chapter 2 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 Over Chapter 2 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 Over Lesson 3–4 containing the point (5, –2) in point-slope form? A. B. C. D. Over Lesson 3–4 What equation represents a line with slope –3 containing the point (0, 2.5) in slope-intercept form? A. y = –3x + 2.5 B. y = –3x C. y – 2.5 = –3x D. y = –3(x + 2.5) Over Lesson 3–4 containing the point (4, –6) in slope-intercept form? A. B. C. D. Over Lesson 3–4 A. B. C. D. Geometry I've got a theory that if you give 100 percent all of the time, somehow things will work out in the end. Larry Bird Assignment: • 3.5 p 210 #6 9-15 odd, 17

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