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Advanced Geometry 5.1

Advanced Geometry 5.1. Indirect proof. 2-Column Proof Form: 2-column format Begin with the GIVEN statements Goal: Prove a statement directly. Indirect Proof Form: Paragraph form Begin with the PROVE statement Goal: Achieve a contradiction of an assumption to complete the proof.

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Advanced Geometry 5.1

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  1. Advanced Geometry 5.1 Indirect proof

  2. 2-Column Proof Form: 2-column format Begin with the GIVEN statements Goal: Prove a statement directly Indirect Proof Form: Paragraph form Begin with the PROVE statement Goal: Achieve a contradiction of an assumption to complete the proof. 2-Column Proof vs. Indirect Proof

  3. Indirect Proof Procedure • List the possibilities for the conclusion. • Assume that the negation of the desired conclusion is correct. • Write a chain of reasons until you reach a contradiction. • State the remaining possibility as the desired conclusion. DPT CARD

  4. Indirect Proof Example: H Given:⊙O HE is not the perpendicular bisector of DF Prove:DE≇EF o Step 1:(list either/or possibilities) Either DE ≇ EF or DE ≅ EF Step 2:(assume negation of “prove” is correct) Assume DE ≅ EF Step 3:(chain of reasoning until contradiction) Given ⊙ O, draw OD and OF because two points determine a segment. Now OD and OF are congruent because they are radii of ⊙ O. Using our assumption that DE ≅ EF, then points O and E are equidistant from the endpoints of segment DF. Since point H is a collinear point on OE, then that means that HE would be the perpendicular bisector of DF. However this is impossible since we were given that HE is not the perpendicular bisector of segment DF, so DF is not bisected by HE. Step 4:(desired conclusion) ∴ DE ≇ EF E F D

  5. For More Indirect Proof Examples: Study Sample Problems 1 and 2 on p. 212

  6. 5.1 Homework: p. 213 – 214 (1, 2, 5 - 8; 10)

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