### Quadrilaterals

# Quadrilaterals

A quadrilateral is a polygon with 4 sides.

Count the edges of the shapes in the picture. All the polygons in the picture are quadrilaterals.

## Before we begin ;

When we think of a rectangle, a specific shape comes to mind, but there are other shapes that also meet the properties of a rectangle (like a square). The first shape that comes to our mind is our primary shape, but there can be other shapes that also fit the criteria.

# Trapezoid - Trapezium

A trapezoid is a quadrilateral with

**at least two sides parallel**to each other.**The word was used to describe a quadrilateral with no parallel sides in British English, but in American English, it refers to a quadrilateral with one pair of parallel sides. The difference in definitions between British and American English can sometimes lead to confusion.**

**Sqaure is a Trapezoid **

(The other sides not indicated by arrows are also parallel to each other.)

**Rectangle is a Trapezoid**

(The other sides not indicated by arrows are also parallel to each other.)

## A parallelogram is a trapezoid.

(The other sides not indicated by arrows are also parallel to each other.)

## Rhombus is a Trapezoid

(The other sides not indicated by arrows are also parallel to each other.)

## Trapezoid

The shape that comes to mind when we say trapezoid

## Right Trapezoid

Trapezoid with one angle of 90 degrees

## Isosceles Trapezoid

Trapezoid with two equal sides.

# Parallelogram

Polygons with opposite sides parallel to each other are called parallelograms.

## A square is a parallelogram

## A Rectangle is a parallelogram

## A Rhombus is a parallelogram

## A parallelogram

The shape that comes to mind when we say parallelogram

# Rhombus

A quadrilateral with all sides of equal length.

## A Square is a Rhombus

All sides of a square are equal.

## Rhombus

The shape that should come to mind when we say 'rhombus'. The primary shape.

All sides of a Rhombus are equal.

# Rectangles

A quadrilateral with opposite sides parallel and interior angles of 90 degrees is called a rectangle.

Square is a Rectangle

All interior angles of a square are 90 degrees.

## Rectangle

The shape that comes to mind when we say 'rectangle'.

# Kite

Quadrilaterals formed by joining two isosceles triangles base to base (along their non-congruent sides)

## A Square is a Kite

## A Rhombus is a Kite

Why rectangle is not a kite ?

# Quadrilaterals Family Tree

Each of the above shapes has its own unique properties, but they also inherit properties from their parent shapes. For instance, a square is a type of rectangle (because it has right angles), and it's also a type of rhombus (because it has sides of equal length). This makes a square a special case of both these shapes and, by extension, a special case of a parallelogram and a quadrilateral.

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