Question

In the figure, ABCD is a parallelogram such that $AF$ and $CE$ are the bisectors of $\angle DAB$ and $\angle BCD$ respectively, then $AF\parallel CE$.

• 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 $DC$.
$⟹\angle DCE=\angle CEB$ (Alternate Angles) -- (1)
Also since, $ABCD$ is a parallelogram
$\angle A=\angle C$ (Opposite angles of a parallelogram as equal )
As, $AF$ and $CE$ are bisectors of these angles respectively,
$\angle FAB=\angle DCE$ --- (2)
From , $\left(1\right)$ and $\left(2\right)$:
$\angle FAB=\angle CEB$
This means, the corresponding angles formed by lines $CE$ and $FA$ cut by transversal $AB$ are equal
$⟹AF\parallel CE$