Question

In a parallelogram, if a diagonal bisects the angles through which it passes, then the parallelogram is a ___

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

Answer 1

The correct option is B

Rhombus

(i) ABCD is a parallelogram (given)

(ii) Let $\angle ADC=\angle ABC=2x^{\circ }$ (Opposite angles of a parallelogram)

(iii) DB bisects $\angle ADC$ and $\angle ABC$ (given)

(iv) $\therefore \angle ADB=\angle BDC=\angle CBD=\angle DBA=x^{\circ }$

(v) $\Delta ADB$ is Isosceles (base angles are equal)

(vi) $\therefore AD=AB$ (vii) ABCD is a rhombus (all sides are equal)