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 .

Answer 1

this is the answer of this question ..

Answer 2

BQ =CP

Proved Beloiw.

Step-by-step explanation:

Given:

As shown in the figure, P and Q are two points on equal sides AB and AC of an isosceles triangle ABC.

Therefore, AB = AC and AP = AQ.

Thus AB - AP = AC - AQ.

Hence BP = CQ.

Now in triangles BCP and BCQ,

BP = CQ                   [given]

angle B = angle C   [ABC is an isosceles triangle]

and BC is common.

Hence triangles BCP and BCQ are congruent (two and the included angle of one triangle are equal to that of the other).

Therefore BQ = CP which are opposite the equal angles B and C.