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

In a quadrilateral ABCD, AB= AD and CB= CD. Prove that: AC bisects angle BAD

In a quadrilateral ABCD, AB = AD and CB = CD. Prove that : (i) AC bisects angle BAD (ii) AC is perpendicular bisector of BD.

If ABCD is a quadrilateral such that AB = AD and CB = CD , then prove that AC is the perpendicular bisector of BD .

In a quadrilateral ABCD, AB = CD and angle B = angle C . Prove that AC = AB

In a quadrilateral ABCD, AB = CD and angle B = angle C . Prove that AD is parallel to BC.

In quadrilateral ABCD, AB=DC and AD=BC. Prove that the sides AB and DC are parallel to each other.

In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. What type of a quadrilateral is ABCD?

ABCD is a parallelogram. What kind of quadrilateral is it if: (i) AC=CD and AC is perpendicular to BD? (ii) AC is perpendicular to BD but is not equal to it ? (iii) AC=BD but AC is not perpendicular to BD ?

In the following figure is CD the perpendicular bisector of AB ?

Draw a parallelogram ABCD, with AB=6cm, AD=4.8 cm and angleDAB=45^(@) . Draw the perpendicular bisector of side AD and let it meet AD at point P. also, draw the diagonals AC and BD, and let them intersect at point O. join O and P. measure OP. DC=5 cm