Chapter 5 1 write indirect proofs
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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 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.

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Chapter 5 1 write indirect proofs

Chapter 5.1

Write Indirect Proofs


Indirect proofs are
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.


Given db ac m is midpoint of ac prove ad cd

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.


Rules
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.


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


Given h k prove jh jk
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


Given math is a square in terms of a find m and a
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)


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