Question

State true or false:

In the fig below. ABCD is a parallelogram. AF and CE are the bisectors of $\angle DAB$ and $\angle BCD$ respectively, then $\angle FAB=\angle CEB$

• A. True
• B. False

Answer 1

The correct option is A True

Since $ABCD$ is a parallelogram, $AB\parallel CD$ as opposite sides of a parallelogram are parallel.
And $CE$ is the transversal passing through $AB$ and $DC$
$\Rightarrow \angle DCE=\angle CEB$ ... (Alternate Angles) $\left(1\right)$
Also, since $ABCD$ is a parallelogram
$\Rightarrow \angle A=\angle C$ .... (Opposite angles of a parallelogram are equal )
As $AF$ and $CE$ are bisectors of these angles respectively,
$\Rightarrow \angle FAB=\angle DCE$ ..... $\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$
$\angle FAB=\angle CEB$