Question

In the given figure, equal sides BA and CA of triangle ABC are produced to Q and P respectively such that AP = AQ. Prove that PB=QC.

Answer 1

consider triangle PAB and triangle QAC,
AP=AQ[GIVEN]
angle PAB=angle QAC[vertically opposite angle]
AB=AC
by SAS congruence these triangles are equal 
so we can say PB = QC[CPCT]

Answer 2

Hope the given picture helps!!