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Question

In the adjoining figure P and Q are two points on equal sides AB and AC of an isosceles triangle ABC such that AP = AQ , prove that BQ = CP
1387309_dbbfbe1ebcee4b7584c9a08b647396b9.PNG

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Solution

REF. Image.
Given AB=AC
and AP=AQ
Thus
AB-AP=AC-AQ
[BP=CA ] [from figure ]
now InΔBCP & ΔBCQ
BP = CQ
c=c [common]
and BC=BC [common]
ΔBCPΔBCQ [SAS congruency]
now
[BQ=CP] [corresponding parts of congruent triangles]

1201986_1387309_ans_5649389ab9b240248cd2fcf84d967c0c.JPG

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