abc is an isosceles triangle in which ab=ac.ad bisects exterior angle pac and cd is parallel to ab.show 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.