Question

State True or False-

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. $△ABE$ is similar to $△CFB$:

• A. Always true
• B. May be true
• C. Information insufficient
• D. Always false

Answer 1

The correct option is A Always true

Let $\angle EBA=x$ and $\angle EAB=y.$
Then, $\angle EAB=\angle FCB$ (Opposite angles of parallelogram)

Also, $\angle EBA=\angle CFB$ ($\because CF||AB$ )

$\Rightarrow \angle AEB=\angle CBF$

Therefore by AAA Theorem of similarity,

$\Delta BCF$ and $\Delta BAE$ are similar.