Question

If the diagonal BD of a parallelogram bisects $\angle$B and $\angle$D, then ABCD is a

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

Answer 1

The correct option is B

Rhombus

ABCD is a parallelogram (given)

$\angle$B = $\angle$D = 2x° (say) … (opposite angles of a parallelogram are equal)

Therefore $\angle$ADB =$\angle$BDC = $\angle$ABD = $\angle$DBC = x° ....(DB bisects $\angle$B and $\angle$D)

ADB is isosceles …...(base angles are equal to x°)

Therefore, AD = AB ……. (equal sides of an isosceles triangle)

ABCD is a rhombus ….. (all sides of the parallelogram are equal)