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# In the figure above, QRS is a straight line and line TR

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Intern
Joined: 04 Aug 2011
Posts: 48

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In the figure above, QRS is a straight line and line TR [#permalink]

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06 Aug 2011, 04:46
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14% (00:25) correct 86% (00:23) wrong based on 14 sessions

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In the figure above, QRS is a straight line and line TR bisects PRS, Is it true that lines TR and PQ are parallel?

(1) PQ=PR (2) QR=PR

pls see the picture attached
[Reveal] Spoiler: OA

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Manager
Joined: 14 Mar 2011
Posts: 198

Kudos [?]: 129 [0], given: 21

Re: A math problem, pls help to solve it ... [#permalink]

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06 Aug 2011, 18:25
To prove that both lines are parallel we need to prove that angle PQR is equal to angle TRS.

statement 1 says)PQ=PR , so angle PQR and angle PRQ are equal. let them be equal to x. Then angle QPR = 180-2x and exterior angle PRS = x+ 180 -2x , so angle PRS = 180-x. TR is bisector of angle angle PRS so angle TRS = half of angle PRS. so angle TRS - 90 -x/2. from this we cant conclude weather 90 -x/2 = x or not. so insufficient.

statement 2 says QR=PR, so angle angle PQR = angle QPR, AND FROM PROPERTY OF EXTERIOR ANGLE =SUM OF TWO INTERIOR ANGLE WE KNOW. angle PRS = angle PQR +angle QPR . so angle TRS = half of angle PRS = angle PQR. so suffiecient. both lines are parallel.

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Re: A math problem, pls help to solve it ...   [#permalink] 06 Aug 2011, 18:25
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