Question

24. In a triangle ABC, the internal bisector of angle A
meets opposite side BC at point D. Through
vertex C, line CE is drawn parallel to DA
which meets BA produced at point E. Show
that A ACE is isosceles.....................​

Answer 1

Answer:

Hi friend

Hope this answer helps you

△ACE is an Isosceles triangle.

Step-by-step explanation:

Given: △ABC, AD bisects ∠BAC, CE∥DA meets AB produced at E

To prove: ACE is an Isosceles triangle

Since, AD bisects ∠BAC

∠BAD=∠DAC

Now, AD∥CE

∠BAD=∠AEC (Corresponding angles)

and, ∠DAB=∠ACE (Alternate angles)

Thus, ∠AEC=∠ACE=∠BAD=∠DAC

In △ACE,

∠AEC=∠ACE

thus, AC=AE (Sides opposite to equal angles are equal)

Hence, △ACE is an Isosceles triangle.