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Organizing a Proof 4-2C How do you write out a proof? What are the three methods that can be used to write a proof? What is a proof? The employee at Best Buy asked for proof of the purchase. The detective found fingerprint proof to use in the robbery case. A Proof—a sequence of true facts (statements) placed in a logical order. How do we convince others that a proof is valid (true)? We supply a reason to justify each statement. Those reasons include: The hypothesis (Given) Information that can be assumed from a figure Definitions Postulates and algebra properties Theorems that have already been proved. If AC and BD bisect each other at M, then AMB CMD Given: AC and BD bisect each other at M Prove: AMB CMD A B Statements 1. AC AND BD bisect each D M Reasons 1. Given other at M 2. AM MC , BM MD 2. Def of bisect 3. AMB DMC 3. Vertical angles cong. 4. AMB CMD 4. SAS Postulate C Formats for Deductive Proofs • Two column ** Statements and reasons columns (p.268) • Paragraph Uses plan and proof paragraphs (p. 267) • Flow chart Statements and reasons are given in boxes and linked by arrows. (p. 268) Convince Me! Given: 1 4, B E AC CD, 5 6 Prove: ABC DEC Statements 1.1 4, AC CD, 5 6 2.1& 2 form linear pair 1 2 5 6 C A 3 4 D Reasons 1.Given 2.Def linear pair 3 & 4 form linear pair 3.1supp. to2, 3 supp. to4 3.Supp cong angles cong 4.ABC DEC 4.ASA Complete the Proof Given: X is the midpoint of VZ 1 2 Prove: VXW ZXY W Z 1 X 2 V Y Statements Reasons a. Supp of cong 1.X is the midpt of VZ b 1. ___ 2.VX XZ 3. WXV YXZ d 2. ___ 4. 1 2 5. VXW ZXY b 4. ___ e 3. ___ c 5. ___ angles cong b. Given c. SAA d. Def of midpt e. Vert angles cong f. Rt angles cong • How do you write out a proof? Use two columns with one for Statements and the other for Reasons • What are the three methods that can be used to write a proof? Two column Paragraph Flow chart Assignment Page 270, 1-2, 4-5, 11-13, 15-16