Question

in triangle ABC, Pand Qare points on BC such that BQ=CP and AP=AQ show that AB=AC

Answer 1

In triangle APB& triangle ACQ
BP=CQ(Subtracting PQfrom both sides)
AP=AQ(Given)
and angle APB=Angle AQC(Since AP=AQ, therefore ANGLE AQP=ANGLE APQ, SO FROM LINEAR PAIR, SUBTRACT THESE ANGLES)
Therefore triangle APB is congruent to Triangle ACQ
Therefore AB=AC(C.P.C.T)

Answer 2

to prove: AB=AC.

proof: In triangle ABQ and triangle APC.
AP= AQ.
so, in triangle APC angle APQ=angle AQP.
angles opposite to equal sides are equal.
BQ=PC.
so, by SAS criteria.
triangle ABQ is congruent to triangle APC.
so , by c.p.c.t. AB=AC.
Hence, proved.