abc is an isosceles triangle in which bisects exterior angle pac and cd is parallel to that angle dac=angle bca and show that abcd is a parallelogram

Let us observe the following figure.

Since ABC is an isosceles triangle we have AB = AC.

AD is the bisector of external and CD is parallel to AB.

In a triangle an exterior angle is equal to the sum of two opposite interior angles.

Thus in triangle ABC, we have

Since AC intersects lines AD and BC at A and C respectively such that , alternate interior angles are equal.

Therefore, AD is parallel to BC.

Given that CD is parallel to AB.

Thus, ABCD is a parallelogram.

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