1 / 11

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.

tovi
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related