In quadrilateral ABCD, AB = AD and CB = CD. Prove that AC is perpendicular bisector of BD.

In the given figure : AB // FD, AC // GE and BD = CE; prove that :

(i) BG = DF

(ii) CF = EG.

In the following figure, BL = CM. Prove that AD is a median of triangle ABC.

In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB. Prove that :

(i) BD = CD

(ii) ED = EF