# Can a rectangle be a rhombus?

Nov 15, 2015

Only if the rectangle is a square

#### Explanation:

A rectangle is a parallelogram with all its interior angles being 90 degrees.

A rhombus is a parallelogram with all its sides equal.

This means that for a rectangle to be a rhombus, its sides must be equal. When this is satisfied, we have a square.

May 18, 2018

A rectangle can be a rhombus only if has extra properties which would make it a square.

#### Explanation:

A rectangle and a rhombus are both types of parallelograms.

However they have different properties of their sides, angles and diagonals.

A rectangle has all its angles 90°
A rectangle has two pairs of equal sides - two longer sides and two shorter sides.
The diagonals of a rectangle are equal, but do not intersect at 90°

The opposite angles of a rhombus are equal. There are two obtuse angles and two acute angles.
All four sides of a rhombus are equal.
The diagonals are not equal, but they intersect at 90°

A rectangle is therefore not a rhombus,

If it is to be a rhombus, additional properties have to be present.
The only time this would happen is if the shape was a square.

A square is a rectangle, but a rectangle is not a square.