# A Rectangle Is A Parallelogram

Given: WXYZ is a parallelogram, ZX ≅ WY Prove: WXYZ is a rectangle What is the missing reason in Step 7? Triangle angle sum theorem. Quadrilateral angle sum. A parallelogram is a quadrilateral with opposite sides parallel. But there are various tests that can be applied to see if something is a parallelogram. It is the 'parent' of some other quadrilaterals, which are obtained by adding restrictions of various kinds: A rectangle is a parallelogram but with all four interior angles fixed at 90°.

*(Jump to Area of a Parallelogram or Perimeter of a Parallelogram) *

A Parallelogram is a flat shape with opposite sides parallel and equal in length.

and show equal sides

Opposite sides are parallel |

Opposite sides are equal in length |

Opposite angles are equal (angles 'a' are the same, and angles 'b' are the same) |

Angles 'a' and 'b' add up to 180°, so they are supplementary angles. |

Play with a Parallelogram:

## A Rectangle Is A Parallelogram With A Right Interior Angle

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

### Example:

A **parallelogram** where all angles are right angles is a **rectangle**!

## Area of a Parallelogram

The Area is the Area = b × h ( |

### Example: A parallelogram has a base of 6 m and is 3 m high, what is its Area?

Area = 6 m × 3 m = **18 m ^{2}**

## Perimeter of a Parallelogram

The Perimeter is the distance around the edges.

The Perimeter is Perimeter = 2(b+s) |

### Example: A parallelogram has a base of 12 cm and a side length of 6 cm, what is its Perimeter?

Perimeter = 2 × (12 cm + 6 cm) = 2 × 18 cm = **36 cm**

## Diagonals of a Parallelogram

The diagonals of a parallelogrambisect each other.

In other words the diagonals intersect each other at the half-way point.

## Inside Any Quadrilateral

And there is a parallelogram in any quadrilateral.

Home >> Parallelogram >> Difference & Similarity between Rectangle & Parallelogram >>## Difference & Similarity between Rectangle & Parallelogram

## A Rectangle Is A Parallelogram True Or False

Area of Parallelogram | Opposite Angles of Parallelogram | Adjacent Angles of Parallelogram | Diagonal Of Parallelogram | Difference & Similarity between Rectangle & Parallelogram |

Difference & Similarity between Square & Parallelogram | Difference & Similarity between Square, Rectangle & Parallelogram | Properties of Parallelogram |

## A Rectangle Is A Parallelogram

Hence, you can observe that there 6 similarities between a Rectangle and a Parallelogram.The highlighted part is the difference between a Rectangle and a Parallelogram. |