Question

ABCD is a parallelogram, if the two diagonals are equal, then measure of $\angle ABC$ is :

• A. ${45}^o$
• B. ${60}^o$
• C. ${90}^o$
• D. ${135}^o$

Answer 1

The correct option is C ${90}^o$

Since ABCD is a parallelogram. Therefore,

$AB=CD$ and $AD=BC$

Thus, in $△$ABD and $△$ ACB,

$AD=BC$

$BD=AC$

$AB=AB$

So, by SSS criterion of congruence,

$△ABD\cong △ACB$

Therefore, $\angle BAD=\angle ABC$

Now, $AD\parallel BC$ and transversal AB intersects them at A and B respectively.

Therefore,

$\angle BAD+\angle ABC={180}^o$

$\angle ABC+\angle ABC={180}^o$

$2\angle ABC={180}^o$

$\angle ABC={90}^o$

Hence, the measure of $\angle ABC$ is ${90}^o$.