In a triangle ABC, AB = AC and ∠A = 36°. If the internal bisector of ∠C meets AB at point D, prove that AD = BC.

If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

In the given figure, AB = AC and ∠DBC = ∠ECB = 90°.

Prove that :

(i) BD = CE

(ii) AD = AE

In triangle ABC; AB = AC. P, Q and R are mid-points of sides AB, AC and BC respectively. Prove that :

(i) PR = QR

(ii) BQ = CP