Question

5. In Fig. 9.43, 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.
pposite to equal sides are equal.
4.
A
P.
Q
С
B
Fig. 9.43​

Answer 1

Answer:

Given AB=AC

and AP=AQ

Thus

AB-AP=AC-AQ

[BP=CA ] [from figure ]

now InΔBCP & ΔBCQ

BP = CQ

∠c=∠c [common]

and BC=BC [common]

∴ΔBCP≃ΔBCQ [SAS congruency]

now

[BQ=CP] [corresponding parts of congruent triangle