##### Asked by: Zhong Jakimovich

asked in category: General Last Updated: 26th May, 2020# Is rhombus always a parallelogram?

**always**the shape above it as well. So a

**rhombus**is

**always a parallelogram**, a square is

**always**a rectangle, and

**always a parallelogram**, and

**always**a quadrilateral, etc.

Considering this, is a rhombus always a parallelogram yes or no?

**Yes**, a **rhombus** is a quadrilateral with 4 equal sides. **Every** square has 4 equal length sides, so **every** square is a **rhombus**. A **parallelogram** is a quadrilateral with 2 pairs of parallel sides. The opposite sides on **every** square are parallel, so **every** square is a **parallelogram**.

Beside above, is a square always a parallelogram? A **square** is a **parallelogram**. This is **always** true. Â Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides.

In this way, is a parallelogram a rhombus?

DEFINITION: A **rhombus is a parallelogram** with four congruent sides. THEOREM: If a **parallelogram** is a **rhombus**, each diagonal bisects a pair of opposite angles. THEOREM Converse: If a **parallelogram** has diagonals that bisect a pair of opposite angles, it is a **rhombus**.

Is a parallelogram always a trapezoid?

It depends. A **Parallelogram** is a quadrilateral with two ses of parallel sides. If you use definition A then **parallelograms** and **trapezoids** are mutually exclusive, that is it is impossible to be both. So under definition A, a **parallelogram** is never a **trapezoid**.