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.

Figure

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

Figure

Global Expert · Accepted Answer

Given: AB=AC △ABC is an isosceles triangle
AP= AQTo prove:BQ=CPProof:AB=AC   (given)AP=AQ   (given)AB-AP=AC-AQ =>BP=CQ∠ABC=∠ACB     (angle opposite to the equal sides are equal)=>∠PBC=∠QCBIn △PBC and△QCB:PB=QC       (proved above)∠PBC=∠QCB    (proved above)BC=BC        (common)By SAS congruence property:△PBC ≅△QCBBQ=CP         (corresponding parts of the congruent triangles)

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. Figure

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.

Figure