Question

Justify the given statement: Rhombus is a parallelogram

Answer 1

Hint: To show that rhombus is a parallelogram, we need to prove that it has the same properties as that of a parallelogram and check the same with the help of a diagram.

Complete step-by-step answer:

Properties that both rhombus and parallelogram possess includes:
1) Both rhombus and parallelogram are quadrilaterals.
Quadrilaterals are those that have 4 sides, 4 vertices and 4 angles sum of which is 360°
2) The opposite sides are parallel and equal (All sides of rhombus are equal) in both the cases.
3) The opposite angles of both the quadrilaterals are equal.
4) The two diagonals formed bisect each other in both rhombus as well as parallelogram.
As all these properties possessed by rhombus are also possessed by parallelograms, we can say that rhombus is a parallelogram and hence the given statement is justified.
Sum of its two adjacent angles is 180 degrees.
It is also called a diamond or rhombus diamond.
Its diagonals bisect each other at 90 degrees and also bisect the angles.
If the mid points of the sides of rhombus are connected, we get a rectangle with area equal to half as that of a rhombus
A square is also a type of rhombus.
→ Both square and rectangle can also be considered as parallelograms due to the similarity between the properties.

Note: Rhombus is a special case of parallelogram.
All rhombuses are parallelograms but all parallelograms are not rhombuses.