MCQ
Rhombus is a quadrilateral.
- AIn which diagonals are inclines at an angle of $60^\circ .$
- BIn which diagonals are equal.
- CIn which diagonals are inclines at an angle of $120.$
- ✓In which diagonals bisect opposite angles.
Let $ABCD$ be a rhombus.
Join $BD$ which forms two triangles $ABD$ and $DCB$. In $\triangle\text{ABD, AB = AD}.$
So, $\angle\text{ADB} = \angle\text{ABD}$ (angles opposite to equal sides are equal) $...(i)$
But, $\angle\text{ABD} = \angle\text{BDC}$ and $\angle\text{ADB} = \angle\text{CBD}$ (alternate angles)$ ...(ii)$
So, from $(i)$ and $(ii)$
$\angle\text{ADB} = \angle\text{ABD}=\angle\text{BDC} = \angle\text{CBD}$
$\therefore$ diagonal $BD$ bisects $\angle\text{B}$ and $\angle\text{D}.$
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