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 $\angle\text{D}.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The expression $x^4 + 4$ can be factorized as $:$
→Every point on a number line represents:
- a rational number.
- a natural number.
- an irrational number.
- a unique number.
In the given figure, O is the centre of a circle. Then, $\angle\text{OAB}=?$
→- 50°
- 60°
- 55°
- 65°
The volume of a sphere of radius $10.5\ cm$ is:
→The equation of the y-axis is:
If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is:
- Equilateral
- Isosceles
- Scalene
- Right-angled
The number of cubes of side 3cm that can be cut from a cuboid of dimensions 10cm × 9cm × 6cm, is:
The number of angles formed by a transversal with a pair of parallel lines are.
In fig ABCD is a parallelogram. If $\angle\text{DAB}=60^\circ$ and $\angle\text{DBC}=80^\circ$ then $\angle\text{CDB}$ is:
→