Question

in the given figure. ABC is an isosceles∆ with AB = AC and CP || BA and AP is the bisector of ext.angle CAD of ∆ABC.prove that

1)Angle PAC = BCA
2)ABPC is a parallelogram​

Answer 1

Answer:

PLS mark my ans as the brainliest

Step-by-step explanation:

ΔABC is isosceles, and AB = AC

let, ∠ABC =∠ACB = x°

∴ ∠CAD = 2x     [exterior angle property]

as PA is the bisector ∴∠PAC = ∠DAP = x each

clearly, ∠PAC = ∠BCA = x

Hence we can conclude that ∠PAC = ∠BCA

2)  to prove that  ABPC is a parallelogram we have to prove that its opposite sides are parallel

from the first proof we got ∠ PAC= ∠BCA

∴ we can say that AP ║ BC  as ∠ PAC= ∠BCA are alternate angles

and it is already given that CP || BA

                                     HENCE PROVED