Parallelogram And Rectangle

There are many different kinds of quadrilaterals, but all have several things in common: all of them have four sides, are coplanar, have two diagonals, and the sum of their four interior angles equals 360 degrees. This is how they are alike, but what makes them different?

We know many quadrilaterals by their special shapes and properties, like squares. Remember, if you see the word quadrilateral, it does not necessarily mean a figure with special properties like a square or rectangle! In word problems, be careful not to assume that a quadrilateral has parallel sides or equal sides unless that is stated.

A parallelogram is a quadrilateral whose opposite sides are equal and parallel. There are 3 main types of parallelograms which are square, rectangle and rhombus. A rectangle is a parallelogram that has four opposite, parallel, congruent sides. The corners of the rectangle form a right angle. The only difference between a rectangle and a square is that the.

Special Quadrilaterals

A parallelogram has two parallel pairs of opposite sides.
A rectangle has two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides.
A square has two pairs of parallel sides, four right angles, and all four sides are equal. It is also a rectangle and a parallelogram.
A rhombus is defined as a parallelogram with four equal sides. Is a rhombus always a rectangle? No, because a rhombus does not have to have 4 right angles.
Trapezoids only have one pair of parallel sides. It's a type of quadrilateral that is not a parallelogram. (British name: Trapezium)
Kites have two pairs of adjacent sides that are equal.

We can use a Venn diagram to help us group the types of quadrilaterals.

A Venn diagram uses overlapping circles to show relationships between groups of objects. All 'quadrilaterals' can be separated into three sub-groups: general quadrilaterals, parallelograms and trapezoids.

Is a rectangle always a rhombus? No, because all four sides of a rectangle don't have to be equal. However, the sets of rectangles and rhombuses do intersect, and their intersection is the set of squares—all squares are both a rectangle and a rhombus.

Parallelogram

We can put squares in the intersection of the two circles.

From this diagram, you can see that a square is a quadrilateral, a parallelogram, a rectangle, and a rhombus!

Is a trapezoid a parallelogram? No, because a trapezoid has only one pair of parallel sides. That is why we must show the set of trapezoids in a separate circle on the Venn diagram.

Area Of Rectangles And Parallelograms

What about kites? Kites are quadrilaterals that can be parallelograms. If their two pairs of sides are equal, it becomes a rhombus, and if their angles are equal, it becomes a square.

Related Links:
Area Formulas
Perimeter Formulas

(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

Parallelogram and rectangle formulas
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:

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

Parallelogram And Rectangle Have In Common

Parallelogram and rectangle formulas

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

The Perimeter is the distance around the edges.

Parallelogram And Rectangle

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

Perimeter = 2(b+s)

Parallelogram and rectangle have in common

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

Parallelogram That Is Not A Rectangle

The diagonals of a parallelogrambisect each other.

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

Parallelogram And Rectangle

Inside Any Quadrilateral

Area Of A Parallelogram Vs Rectangle

And there is a parallelogram in any quadrilateral.