Question

ABC is an isosceles triangle in which AB=AC. AD bisects exterior angle PAC and CD parallel to AP. SHOW THAT AD PARALLEL TO BC ( please answer fast )

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given : ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle PAC and CD∣∣AP.

To show :

AD PARALLEL TO BC

Proof :

(i)

∠ABC=∠BCA=y(let) (Because triangle ABC is an isosceles triangle)

∠PAD =∠DAC = x (let) (Given)

∠DCA =∠BAC = z (let) (Alternate interior angles)

And we know that an exterior angle of a triangle is equal to the sum of the opposite interior angles.

So,

∠PAD+∠DAC=∠ABC+∠BCA

x + x = y + y

2x = 2y

x = y

∠DAC = ∠BCA (hence proved)

(ii)

Now because,

∠DAC=∠BCA (proved above)

Therefore , AD∣∣BC

Also, CD∣∣AB (Given)

Since opposite sides of quadrilateral ABCD are parallel therefore ABCD is a parallelogram.