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Question

In the given figure, RS=QT and QS=RT. Then which of the following options is correct?




A

PQ=PR

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B

PR=TR

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C

PQ=QS

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D

None of these

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Solution

The correct option is A

PQ=PR


In ΔRSQ and ΔQTR
RS=QT [given]
RT=SQ [given]
RQ=RQ [common]
Thus, ΔRSQΔQTR [by SSS congruence rule]
1=2 [CPCT]
3=4 [vertically opposite angles]
5=6
Now, in ΔPSQ and ΔPTR
QS=RT [given]

1+7=2+8 [supplementary angles]
So, 7=8 [1=2]
6=5 [already proved]

ΔPSQΔPTR [by AAS congruence rule]
PQ=PR [CPCT]


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