Question

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

Answer 1

hey
____

hence , BQ = CP ( prooved by c.p.c.t)

refer to the attachment for the ans

hope helped
_____________

Answer 2

Consider ΔAPQ∆APQ and ΔABC∆ABC

Given that AP=AQAP=AQ

APAB=AQACAPAB=AQAC and ∠PAQ=∠BAC∠PAQ=∠BAC

Hence by SAS theorem, ΔAPQ∼ΔABC∆APQ∼∆ABC

Hence, by converse of BPT theorem,

PQ||ABPQ||AB

Hence, ∠APQ=∠AQP∠APQ=∠AQP (isosceles triangle).

⟹∠BPQ=∠CQP...(1)⟹∠BPQ=∠CQP...(1)

Since it is given that AP=AQAP=AQ and AB=ACAB=AC, AB−AP=AC−AQAB−AP=AC−AQ i.e. PB=PQ....(2)PB=PQ....(2)

Consider ΔBQP∆BQP and ΔCPQ∆CPQ.

PQ=QPPQ=QP

∠BPQ=∠CQP∠BPQ=∠CQP from (1)(1)

PB=QPPB=QP from (2)(2)

Hence,

ΔBPQ≅ΔCQP∆BPQ≅∆CQP

Hence,

BQ=CP


Plz mark as brainliest and Leave a thanks.
.....With Regards from
#@Jai