Question

Which of the following statements are true?

• A. Adjacent angles of a parallelogram are supplementary
• B. Diagonals of a parallelogram bisect each other
• C. A parallelogram with one right angle is a rectangle
• D. Diagonals of a parallelogram are equal in length

Answer 1

Answer: (A), (B), (C)

The correct options are
A

Adjacent angles of a parallelogram are supplementary

B

Diagonals of a parallelogram bisect each other

C

A parallelogram with one right angle is a rectangle

The diagonals of a parallelogram bisect each other, but the diagonals need not be of equal length in general.

Also, using the fact that opposite angles are equal, from the figure, we have $2x+2y={360}^{\circ }$ .
$⟹x+y={180}^{\circ }$
Thus, $x$ and $y$ are supplementary.

Also, if one angle of the parallelogram is right angle , then its opposite angle is also right angle. Now, using the fact that consecutive angles are supplementary, we get that all angles of the parallelogram are right angles .

Thus, the parallelogram is a rectangle.