In the adjoining figure AC = AE, AB = AD and ∠BAD = ∠CAE. Show that BC = DE.

In the adjoining figure, AB = AC and D is the midpoint of BC. Use SSS rule of congruency to show that

(i) △ABD ≅ △ACD

(ii) AD is bisector of ∠A

(iii) AD is perpendicular to BC.

In the adjoining figure, AB = DC and AB || DC. Prove that AD = BC.

Two line segments AB and CD bisect each other at O. Prove that

(i) AC = BD

(ii) ∠CAB = ∠ABD

(iii) AD || CB

(iv) AD = CB