Question
Rhombus is a quadrilateral.
✓
Answer
- In which diagonals bisect opposite angles.
Solution:
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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