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.

Two line segments AC and BD bisect each other at P. Draw the diagram and prove that

(i) AB = CD

(ii) ∠BAC = ∠DCA

Prove that the median drawn from the vertex P of an isosceles triangle △PQR with PQ = PR is perpendicular to QR and bisects ∠P.