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G.6 Lesson 3, 2 column proofs.notebook November 21, 2016 Do Now: Find the measure of all 4 angles (not drawn to scale) x2 15 2x G.6 Lesson 3 -- 2-Column Proofs Learning Target: Today I will be able to use the 2-column proof method of deductive reasoning to prove a statement and will do this by building a “library of justifications” and collaboratively proving two statements before individually completing a proof as an exit ticket with 6 out of 8 steps justified correctly. SOL - G.6 Homework: page 247, #9, 16, 19 G.6 Lesson 3, 2 column proofs.notebook November 21, 2016 Step 1: Build a library of "justifications" to use when proving statements. *This library is based on what we've already learned and should grow throughout the year. Library of Justifications Properties of Equality • addition • subtraction • multiplication • division Substitution Property Transitive Property Linear Pair Postulate Reflexive Property Alt Interior Angles Theorem Symmetric Property CPCTC Distributive Property Various "keyword" definitions Angle Addition Postulate Segment Addition Postulate Vertical Angle Theorem G.6 Lesson 3, 2 column proofs.notebook November 21, 2016 Addition Property of equality a+c=b+c Subtraction Property of equality Multiplication Property of equality a - c = b -c If a = b, then axc=bxc Division Property of equality if Properties of Equality Reflexive Property Symmetric Property Transitive Property a=a If a = b, then b = a If a = b and b = c, then a = c then G.6 Lesson 3, 2 column proofs.notebook Distributive Property Substitution Property November 21, 2016 a(b+c) = ab + ac a(b-c) = ab - ac If a = b, then b can replace a in any expression. Vertical Angles Theorem Vertical Angles are congruent Segment Addition Postulate AB + BC = AC Angle Addition Postulate m<ABC + m<CBD = m<ABD Linear Pair Postulate Two linear angles are supplementary Definitions are valid justification as well G.6 Lesson 3, 2 column proofs.notebook November 21, 2016 Step 2: Learn how to construct and justify a 2column proof. We'll start by simply solving a problem as we've always done, but....we'll add a justification for each step. B 3x Solve, justifying each step 2x + 6 A WB p. 51, #2, 3 C D G.6 Lesson 3, 2 column proofs.notebook November 21, 2016 Now, we'll do a fullup proof. With a proof we have a hypothesis (the "given") and a conclusion. We just have to get from p to q! If M is the midpoint of a line segment, then x=2. Given: M is the midpoint of AB, AM=4x+2, MB=2x+6 M Prove: x=2 B 2x+6 A 4x+2 M is the midpoint of AB AM=4x+2, MB=2x+6 AM = MB 4x + 2 = 2x + 6 2x + 2 = 6 2x = 4 x=2 G.6 Lesson 3, 2 column proofs.notebook November 21, 2016 Properties of Geometric Parts Reflexive Property Symmetric Property Transitive Property If then If then If and then If and then Do Now: List the 5 theorems/postulates available to prove two triangles congruent. Then list the two combinations that DON'T work to prove triangles congruent. Then find the lengths of all sides of the two triangles shown. D A (4, 7) 2x 4x C B (4, 13) F 3x E G.6 Lesson 3, 2 column proofs.notebook November 21, 2016 G.6 Lesson 3 -- 2-Column Proofs Learning Target: Today I will be able to use the 2-column proof method of deductive reasoning to prove a statement and will do this by building a “library of justifications” and collaboratively proving two statements before individually completing a proof as an exit ticket with 6 out of 8 steps justified correctly. SOL - G.6 Homework: page 247, #9, 16, 19 G.6 Lesson 3, 2 column proofs.notebook November 21, 2016 , G.6 Lesson 3, 2 column proofs.notebook November 21, 2016 G.6 Lesson 3, 2 column proofs.notebook November 21, 2016 G.6 Lesson 3 -- 2-Column Proofs Learning Target: Today I will be able to use the 2-column proof method of deductive reasoning to prove a statement and will do this by building a “library of justifications” and collaboratively proving two statements before individually completing a proof as an exit ticket with 6 out of 8 steps justified correctly. SOL - G.6 Homework: page 247, #9, 16, 19 Exit ticket: Complete the following using 2-column proof format A D B Given: ∠ABC and ∠DBE are vertical angles 3x+1 6x‐2 And m∠ABC=3x+1 and m∠DBE=6x‐2 Prove: x = 1 Homework: p.247, #9, 16, 19 c E G.6 Lesson 3, 2 column proofs.notebook November 21, 2016