Question

21. I
B
C
12. ABC is an isosceles triangle. P is a point on AB produced
and Q is a point on AC produced such that AP = AQ
Prove that PC = QB.
[Hint: ZPBC = ZQCBI
Р
A​

Answer 1

Answer:

Given ABC is a trianlge in which AB=AC . P is any point in the interior of the triangle such that angle ABP=ACP

In ΔAPB and ΔAPC,

AB=AC[given]

∠ABP=∠ACP [given]

AP=AP[common]

ΔAPB≅ΔAPC[by SAS congruency criterion]

∴∠PAB=∠PAC [corresponding angles of congruent trianlges]

thus, BP=CP

And AP bisects ∠BAC