Question

The bisectors of opposite angles of a parallelogram are parallel.

• A. True
• B. False

Answer 1

The correct option is A True

$\square$$ABCD$ is all gm and $DE$ and $BF$ are angle bisectors.

$\therefore$ $\angle$$B$ = $\angle$$D$

$\therefore$ $\frac{1}{2}$$\angle$B $=\frac{1}{2}$$\angle$D

$\therefore$$\angle$$ADE$$=\angle$$FBC$

In $△$$ADE$ $=△$$FBC$,

$AD=BC$ ( $\because$ opposite sides of llgm are congruent)

$\angle$$ADE$ = $\angle$$FBC$

$\angle$$DAE$ = $\angle$$BCF$ ($\because$ opposite angles of llgm are congruent)

$\therefore$By $ASA$ congruence criterion,

$△$$ADE$$\cong$ $△$$CBF$

$\therefore$ $AE=CF$ => $BE$=$DF$

Also,$DE=BF$

$\therefore$ $\square$$DEBF$is a parallelogram. ( $\because$ opposite sides are congruent)

$\therefore$ $DE$ $\parallel$ $BF$

$\therefore$ $△$DEBF is a parallelogram.($\because$ opposite sides are congruent)

$\therefore$$DE$ $\parallel$$FB$

Hence,the bi rectors of opposite angles of a parallelogram are parallel.

Ans : A) True.