Question

The angle-bisectors of a parallelogram form a quadrilateral as shown in the figure given below,
Then ABCD is a .

• A. Square
• B. Rectangle
• C. Trapezium
• D. Rhombus

Answer 1

The correct option is B Rectangle

PB and SB are the respective angle bisectors of $\angle$P and $\angle$S,
In any quadrilateral the angle bisectors intersect at right angles.
Thus, in $△$PBS, $\angle$PBS = ${90}^{\circ }$
or, $\angle$ABC = $\angle$PBS = ${90}^{\circ }$ (vertically opposite angles)
Similarly,
$\angle$ADC = $\angle$DCB = $\angle$BAD = ${90}^{\circ }$
Since all angles of parallelogram ABCD are 90°,
ABCD is a rectangle.