In the quadrilateral ABCD , AD = BC and `angleBAD = angleABC` . Prove that the quadrilateral is an isosceles trapezium.

In the the cyclic quadrilateral ABCD,AB =CD . Prove that AC= BC

In cyclic quadrilateral ABCD, BC is diamter. If angleABC=62^@ then angleADB =

If in the cyclic quadrilateral AB||CD , then prove that AD =BC and AC=BD.

Prove that an isosceles trapezium is always cyclic.

Two oppsite angles of the quadrilateral ABCD are supplementary and aC bisects angle BAD . Prove that BC Cand CD are equal.

Given that the vertices A, B, C of a quadrilateral ABCD lie on a circle. Also angleA + angleC = 180^@ , then prove that the vertex D also lie on the same circle.

In a cyclic quadrilateral ABCD, AB is a diameter. If angleACD = 50^@ , then angleBAD =

AB is a diameter of a circle. PQ is such a chord of the circle that it is neither a diameter of the circle nor a interceptor of AB. By joining the points A, P and B, Q it is found that ABQP is a quadrilateral of wich angleBAP=angleABQ . Prove that ABQP is a cyclic trapezium.

The quadrilateral ABCD is circumsribed about a circle. Prove that AB+ CD= BC+DA.

The diagonals of the quadrilateral ABCD intersect each other at O in such a way that (AO)/(BO)=(CO)/(DO) . Prove that ABCD is a trapezium.