Question

in a cyclic trapezium the nonparallel sides are equal and the diagonals are also equal prove it

Answer 1

Let ABCD be the cyclic trapezium in which AB||CD.

We have to prove that AD = BC

Since AB||CD and BD is the transversal, we have

∠ABD = ∠BDC [Alternate angles]

Also chord AD subtends ∠ABD and chord BC subtends ∠BDC on the circle at B and D respectively.

Also ∠ABD = ∠BDC (proved above)

Therefore, AD = BC