Question

State true or false:

For the case of a parallelogram the bisectors of opposite angles are not parallel to each other.

• A. True
• B. False

Answer 1

The correct option is B False

GIvem $ABCD$ is a parallelogram.

$DE$ bisect $\angle D,$ $BF$ bisect $\angle B.$

$\Rightarrow \angle D=\angle B$ [ Opposite angles of parallelogram are equal ]

$\Rightarrow \angle 1=\angle 2$ [ Equal angle bisect still equal ]

$\Rightarrow \angle A=\angle C$ [ Opposite angles of parallelogram are equal ]

$\Rightarrow AD=BC$ [opposite sides of parallelogram are equal ]

$\therefore △ADE\cong △CBF$ [ By ASA congruence condition ]

$\Rightarrow DE=BF$ [ By CPCT proved ]

$\therefore$ The statement is false.

Hence, the answer is the statement is false.