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Geometry Section 4-2C Organizing a Proof Pg. 266 Be ready to grade 4-2B

Geometry Section 4-2C Organizing a Proof Pg. 266 Be ready to grade 4-2B. Proof: A sequence of true statements placed in a logical order. Types of statements to include:. The given information. Information that can be assumed from the figure. Definitions.

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Geometry Section 4-2C Organizing a Proof Pg. 266 Be ready to grade 4-2B

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  1. Geometry Section 4-2COrganizing a ProofPg. 266Be ready to grade 4-2B

  2. Proof: A sequence of true statements placed in a logical order. Types of statements to include: The given information. Information that can be assumed from the figure. Definitions Page 839 contains a list of postulates and theorems by chapter. Postulates Algebraic properties Theorems that have already been proven. Every statement you put in your proof must be a result of something from above it.

  3. 3 types of proofs: Paragraph form:

  4. 3 types of proofs: Two-column form:

  5. 3 types of proofs: Flow-proof form:

  6. Important: Mark the illustration as the reasoning progresses. Explore: Given: Ð1 @Ð4 AC @ CD Ð5 @Ð6 Prove: rABC @rDEC B Ð1 and Ð2 form a linear pair, as do Ð3 and Ð4. Thus Ð1 is supplementary to Ð2, and Ð3 is supplementary to Ð4 because E the angles in a linear pair are supplementary. given information The tells us that Ð1 @Ð4. Therefore, Ð2 @Ð3 because supplements of congruent angles are congruent. given information. We also know that AC @ CD, and Ð5 @ Ð 6 from ASA Therefore, we can conclude that rABC @rDEC by the Postulate. 1 2 5 4 6 3 A C D

  7. Important: Mark the illustration as the reasoning progresses. Try It: Given: X is the midpoint of VZ Ð1 @Ð2 Prove: rVXW @rZXY W Z 2 1 X b. Given b. Given c. SAA d. Def. of midpoint e. Vert. Ð’s are @. V Y

  8. Given: rABC and rXYZ are right triangles with right angles ÐA and ÐX. AB @ XYÐB @ÐYProve: rABC@rXYZ B Y Given AB @ XY 1 X A Z C Given ÐA andÐX are rt. angles 2 Rt. Angles are @ ÐA @ÐX 3 Given ÐB @ÐY 4 rABC @rXYZ ASA Therefore, rABC @rXYZ by the ASA Postulate. The given information tells us that AB @ XY ÐA @ÐX because all right angles are congruent. We are also given that ÐB @ÐY And that ÐA and ÐX are right angles.

  9. Given: F is the midpoint of DH and EG.Prove: rDFE@rHFG D E F is midpt. of DH and EG Given F 1 Def. of midpoint DF @ HF 2 EF @ GF Def. of midpoint 3 G H ÐHFG @ÐDFE Vert. angles are @ 4 SAS rDFE @rHFG

  10. Given: PQ || RSPQ @ RSProve: rPQS@rRSQ P Q S R PQ @ RS Given 1 Reflexive SQ @ SQ 2 Given PQ || RS 3 ÐPQS @ÐRSQ Alt. Int. are @ 4 SAS rPQS @rRSQ

  11. Homework: Practice 4-2CSkip the last one.

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