Question

State whether true or false:

In the given figure, AM bisects $\angle A$ and DM bisects $\angle D$ of parallelogram ABCD.

The measure of $\angle AMD={90}^{\circ }$.

• A. True
• B. False

Answer 1

The correct option is A True

Given, AM bisects angle A and DM bisects angle D of parallelogram ABCD.
AB is parallel to DC, so,
$\angle A+\angle D={180}^o$ (Sum of interior angles on the same side of a transversal is supplementary.
AM bisects angle A and DM bisects angle D
$\angle A=2\angle DAMand\angle D=2\angle ADM$
Now, put it in above equality,
$2\angle DAM+2\angle ADM={180}^o$
$\angle DAM+\angle ADM={90}^o$
In $△AMD$
$\angle DAM+\angle ADM+\angle AMD={180}^o$
${90}^o+\angle AMD={180}^o$
$\angle AMD={90}^o$