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Question

In Fig. AB=PQ, BC=RQ, AB=BQ and PQ=BQ Prove that ABRPQC.
1064238_fb89e9324d934de2bc4d175382779244.png

Solution
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Given:AB=PQ=BQ
InABC&PQR
AB=PQ
ABC=PQR=90
BC=RQ
ABCPQR
AC=PR(C.P.C.T)
InABR
AB2+BR2=AR2
AB2+(BC+CR)2=AR2(1)
InPCR:
PQ2+QC2=PC2
PQ2+(QR+CR)2=PC2
In(1)&(2),
AB=PQ(given)
andBC=QR(given)
AR2=PC2(from(1)&(2))
AR=PC(3)
InABR&PQC
AB=PQ
ABR=PQC=90
AR=PC(from(3))
ABRPQCbyR.H.S

1005600_1064238_ans_388c6ff13f78419eb76fb1ba875432b4.png

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