This is just geometry one. we are given that rag ie bisects angle kid and angle ied is congruent to angle iek. we have to prove that triangle kid is isosceles.

Step-by-step explanation:

We are given that IE bisects <KID

Using this, we can say that <EID is congruent to <EIK by the definition of an angle bisector.

We are also given that <IED is congruent to <IEK.

Since these two angles are congruent, we can say that <IDE is congruent to <IKE. This is proven with the 3rd angle theorem.

Since the two base angles are congruent, the triangle is isosceles by the definition of an isosceles triangle.