Question

State true or false:

The following figure shows a trapezium $ABCD$ in which $AB$ is parallel to $DC$ and $AD=BC$, then $\angle DAB=\angle CBA$

• A. True
• B. False

Answer 1

The correct option is A True

Construction to be made: Drop $\perp$ from D to AB & from C to AB.

So $\angle DMA=\angle CNB={90}^o$

Since DC$\parallel$ AB( given ) so DM=CN.

In $△$ ADM & $△$ BCN,\

AD=BC ( given )

DM=CN ( By construction )

$\angle DMA=\angle CNB={90}^o$ ( By construction )

So $△$ ADM $\cong △$ BCN ( By RHS rule of congruency )

$\therefore \angle DAM=\angle CBNor\angle DAB=\angle CBA$