Question

Suppose in a quadrilateral ABCD, AC = BD and AD = BC. Prove that ABCD is a trapezium.

Answer 1

It is given that AC = BD and AD = BC.

Consider ΔABC and ΔABD.

BC = AD (Given)

AC = BD (Given)

AB = AB (Common side)

Therefore, from SSS congruency, we get

_{Since these angles are alternate angles between the lines AB and CD, AB || CD.}

Hence, ABCD is a trapezium.