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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Write Indirect Proofs
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.
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.
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.
What are the coordinates of A and M?
What is the area of MATH?
A = 4a2
What is the midpoint of MT?
T (2a, 0)
H (0, 0)