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Chapter 5.1 Write Indirect Proofs. Indirect Proofs are…? An indirect Proof is used in a problem where a direct proof would be difficult to apply. It is.

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Presentation on theme: "Chapter 5.1 Write Indirect Proofs. Indirect Proofs are…? An indirect Proof is used in a problem where a direct proof would be difficult to apply. It is."— Presentation transcript:

1 Chapter 5.1 Write Indirect Proofs

2 Indirect Proofs are…? An indirect Proof is used in a problem where a direct proof would be difficult to apply. It is used to contradict the given fact or a theorem or definition.

3 Given: DB AC M is midpoint of AC Prove: AD ≠ CD D C MB A T ~ In order for AD and CD to be congruent, Δ ADC must be isosceles. But then the foot (point B) of the altitude from the vertex D and the midpoint M of the side opposite the vertex D would have to coincide. Therefore, AD ≠ DC unless point B  point M.

4 Rules: 1.List the possibilities for the conclusion. 2.Assume negation of the desired conclusion is correct. 3.Write a chain of reasons until you reach an impossibility. This will be a contradiction of either: 1.the given information or 2.a theorem definition or known fact. 4.State the remaining possibility as the desired conclusion.

5 Either RS bisects  PRQ or RS does not bisect  PRQ. Assume RS bisects  PRQ. Then we can say that  PRS   QRS. Since RS PQ, we know that  PSR   QSR. Thus, ΔPSR  ΔQSR by ASA (SR  SR) PR  QR by CPCTC. But this is impossible because it contradicts the given fact that QR  PR. The assumption is false. RS does not bisect  PRQ. T

6 Given:

7 Given: MATH is a square In terms of a, find M and A T (2a, 0) H (0, 0) M A What is the area of MATH? What is the midpoint of MT? (2a, 2a) (0,2a) What are the coordinates of A and M? A = 4a 2 (a, a)


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