Question

In the adjoining fig ,P& Q are two points on equal sides ,AB and AC of an isosceles triangle ABC such that AP = AQ Prove that BQ =AQ

Answer 1

Let the two triangles be, BPQ and CQP.

Now, Since its an isosceles triangle, AB=AC and AP=AQ, which means PB=QC.

Now we can prove that Angle BPQ= Angle PBC and Angle CQP = Angle QCB(Corresponding angles)

If corresponding angles of two triangles are equal, then the third also will be equal in magnitude.

Hence the two triangles are proved to be Congruent.

Hence the third side, also becomes equal.

Hence BQ=CP.

Hope This Helps :)