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. Then/Now

G.CO.9 Prove theorems about lines and angles. 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. CCSS

3.5 Proving Lines Parallel Objectives: 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. corresponding angles alternate interior angles alternate exterior angles consecutive interior angles 1 2 3 4 6 5 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.   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?                

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

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

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

containing the point (5, –2) in point-slope form? B. C. D. 5-Minute Check 1

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) 5-Minute Check 3

containing the point (4, –6) in slope-intercept form? B. C. D. 5-Minute Check 4

A. B. C. D. 5-Minute Check 6

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