Can a rectangle be a rhombus?

Question

Aaliyah Anderson · Accepted Answer

Only if the rectangle is a square

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.

Evelyn Arboleda · Answer

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

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.

Parker Allen · Answer

undefined Yes, a rectangle can be a rhombus. By definition, a rhombus is a quadrilateral with all four sides of equal length, while a rectangle is a quadrilateral with four right angles. Since a square is a special type of rhombus with all angles equal to 90 degrees, it is also a rectangle. Therefore, if all angles of a rectangle are equal (which would make it a square), then it satisfies the criteria for being a rhombus as well. So, every square is both a rectangle and a rhombus. However, not all rectangles are rhombuses, as rectangles have two pairs of opposite sides equal in length, while rhombuses have all four sides equal in length.