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Is a Rectangle a Parallelogram? Or Is a Parallelogram a Rectangle?

is a rectangle a parallelogram: different colors of blocks

Both rectangles and parallelograms are quadrilaterals, which means that they are polygons with four sides. But is a rectangle a parallelogram? Or is a parallelogram a rectangle? Here's a review of the different properties of both parallelograms and rectangles.

A parallelogram is a quadrilateral that has:

  • Two pairs of parallel sides
  • Two pairs of opposite sides that are congruent

A rectangle is a quadrilateral that has:

  • Four right angles
  • Two pairs of opposite sides that are congruent

A rhombus is a quadrilateral that has:

  • Four sides of equal length
  • Two pairs of equal opposite angles

Properties of a Rectangle vs. a Parallelogram

is a rectangle a parallelogram: rectangle vs parallelogram

Image credit: Desmos

When a rectangle has four right angles, all of the interior angles are congruent. The vertices join the adjacent sides at 90° angles, which means the opposite sides of the rectangle are parallel lines. Since it has two sets of parallel sides and two pairs of opposite sides that are congruent, a rectangle has all of the properties of a parallelogram. That’s why a rectangle is always a parallelogram.

However, a parallelogram is not always a rectangle. The below example is of a parallelogram that does not have four right angles. Next, we’ll explain this shape’s properties.

Properties of a Rectangle vs. a Rhombus

rhombus

The shape above is a rhombus, which we defined above. Since a rhombus looks similar to a rectangle, let’s talk about the similarities between the two.

Now, a rectangle is not always a rhombus. A rectangle has two sets of congruent sides whereas all four sides of a rhombus are congruent.

Is a rhombus always a parallelogram though? The answer is yes! The two pairs of opposite angles of a rhombus are always equal, just like the two pairs of opposite angles of a parallelogram are always equal. This means that a rhombus is just a special case of a parallelogram where all four sides happen to also be congruent.

Is a Rectangle a Parallelogram?

Rectangles, parallelograms, and rhombuses are all special quadrilaterals with certain properties.

A parallelogram is a quadrilateral that has:

  • Two pairs of parallel sides
  • Two pairs of opposite sides that are congruent

A rectangle is a quadrilateral that has:

  • Four right angles
  • Two pairs of opposite sides that are congruent

A rhombus is a quadrilateral that has:

  • Four sides of equal length
  • Two pairs of equal opposite angles

There are many more types of quadrilaterals than we’ve covered here. But now you know the answer to the question “Is a rectangle a parallelogram?” A rectangle is always a parallelogram. But a parallelogram is not always a rectangle.

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