Question

ABCD is a trapezium in which AB || CD and AD =BC (see the given figure). Show that Diagonal AC=diagonal BD.

Answer 1

In $\Delta ABC$ and $\Delta ABD$,
AB=BA (Common side)
BC=AD (Given)
$\angle B=\angle A$ (Proved before)
$\Delta ABC\cong \Delta ABD$ (SAS congruence rule).

$\because$ $\Delta ABC\cong \Delta BAD$.
Hence , AC = BD [CPCT].