Question

ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively, such that AB = BE and AD = DF.

Hence $\Delta BEC\cong \Delta DCF$.

State whether the above statement is true or false.

• A. True
• B. False

Answer 1

The correct option is A True

$\angle BAD=\angle CDF$ (Corresponding angles for parallel lines AB and CD)
$\angle BAD=\angle CBE$ (Corresponding angles for parallel lines AB and CD)
Thus, $\angle CDF=\angle CBE$ (I)
We know, $AD=BC$ (ABCD is a parallelogram)
and $AD=DF$ (Given)
Thus, $DF=BC$ (II)
Similarly, $BE=CD$ (III)
Now, In $△CDF$ and $△CBE$
$\angle CDF=\angle CBE$ (From I)
$FD=BC$ (From II)
$BE=CD$ (From III)
Thus, $△FDC\cong △CBE$ (SAS rule)