Question

The diagonal $BD$ of a quadrilateral $ABCD$ bisects $\angle B$ and $\angle D.$ Then $:AB\times CD=AD\times BC.$

If true answer is 1, else 0

Answer 1

In $△ABD$ and $△CBD$,
$BD=BD$ (Common)
$\angle ABD=\angle CBD$ (BD bisects $\angle B$)
$\angle ADB=\angle ADC$ (BD bisects $\angle D$)
Thus, $△ABD\cong △CBD$ (ASA postulate)
Hence, $AB=BC$ and $AD=CD$ (Corresponding sides)
or $AB\times CD=BC\times AD$