1 / 7

Chapter 5.1 Write Indirect Proofs

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 used to contradict the given fact or a theorem or definition. D. Given: DB AC M is midpoint of AC Prove: AD ≠ CD. T. ~. A. C.

buckminster-ward
Download Presentation

Chapter 5.1 Write Indirect Proofs

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. 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. D Given: DB ACM is midpoint of ACProve: AD ≠ CD T ~ A C B M 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: • List the possibilities for the conclusion. • Assume negation of the desired conclusion is correct. • Write a chain of reasons until you reach an impossibility. This will be a contradiction of either: • the given information or • a theorem definition or known fact. • 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:<H ≠ <KProve: JH ≠ JK ~ ~ • Either JH is  to JK or it’s not. • Assume JH is  to JK, then ΔHJK is isosceles because of congruent segments. • Then  H is  to  K. • Since  H isn’t congruent to  K, then JH isn’t congruentto JK. J H K

  7. Given: MATH is a squareIn terms of a, find M and A What are the coordinates of A and M? (2a, 2a) A M (0,2a) What is the area of MATH? A = 4a2 What is the midpoint of MT? T (2a, 0) H (0, 0) (a, a)

More Related