A Rectangle Is A Parallelogram

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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 base times the height:

Area = b × h

(h is at right angles to b)

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

Area = 6 m × 3 m = 18 m2

Perimeter of a Parallelogram

A Rectangle Is A Parallelogram

The Perimeter is the distance around the edges.

The Perimeter is 2 times the (base + side length):

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.

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Difference & Similarity between Rectangle & Parallelogram

A Rectangle Is A Parallelogram True Or False

Rectangle
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


RectangleParallelogram
  • A rectangle is also a quadrilateral
  • A parallelogram is also a quadrilateral
  • Opposite sides of rectangle are parallel to each other
  • Opposite sides of parallelogram are also parallel to each other
  • Opposite angles of rectangle are equal
  • opposite angles of parallelogram are also equal
  • Adjacent angles of rectangle are supplementary
  • Adjacent angles of parallelogram are also supplementary
  • Diagonals of rectangle bisect each other
  • Diagonals of parallelogram also bisect each other
  • Opposite sides of rectangle are of equal length
  • Opposite sides of parallelogram are also of equal length
  • All angles of a Rectangle are also of 90 Degree each i.e. right angled at each vertex
  • Angles of parallelogram can be of different degree
  • Diagonals of Rectangle are of equal length
  • Diagonals of parallelogram are not of equal length

  • 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.