Question

State true or false:

In the alongside diagram, $ABCD$ is a parallelogram in which $AP$ bisects angle $A$ and $BQ$ bisects angle $B$, then

$ABPQ$ is a parallelogram

• A. True
• B. False

Answer 1

The correct option is A True

ABPQ is a parallelogram is the opposite sides are equal and parallel.

AP bisects $\angle A$ and $BQ$ bisects $\angle B.$

Consider $△ABQ$ and $△ABP$

$\Rightarrow \angle A=\angle P$ [ Opposite angle of parallelogram ]

$\Rightarrow AB=QP$

$\Rightarrow \angle x=\angle x$ [ Bisector of opposite angle ]

By ASA $△AQB\cong △ABP$

Then by CPCT, $BP=AQ.$

Hence the distance between AB and PQ are equal.

$\Rightarrow AB\parallel PQ$

$\therefore ABPQ$ is a parallelogram.

$\therefore$ The statement is true.

Hence, the answer is true.