Question

In the figure, ABC is an isosceles triangle in
which AB = AC. The side BA is produced to D
and CP || BA is drawn. The bisector of angle CAD
cuts CP at P. Prove that ABCP is a parallelogram.​

Answer 1

Answer:

angle BAC = angle ACP alternate angle (Since BA || CP And CA is transversal)

Since AB=AC angle ABC = angle ACB

angle CAD = angle ABC + angle ACB

2*angle ABC = angle CAD

angle ABC = 1/2 angle CAD= angle CAP

Now we can prove ∆ABC and ∆ ACP are congruence (A-S-A)

So AB=CP

AP= BC

AP || BC

Hence ABCP is a Parallelogram

Answer 2

ABCP is a parallelogram(proved)