Question

State true or false:

The following figure shows a trapezium $ABCD$ in which $AB$ is parallel to $DC$ and $AD=BC$, then $OA=OB$ and $OC=OD$

• A. True
• B. False

Answer 1

The correct option is A True

In $△AOD$ and $△BOC$ ,

$AD=BC$ (Given)

$\angle ADO=\angle CBO(AB\parallel CD$ & $AC$ traversal)

$\angle DAO=\angle BCO(AB\parallel CD$ & $BD$ traversal)

$\therefore △DAO\cong △BCO$ [By ASA]

Hence, $AO=OB$ & $OD=OC$ [By CPCT]