# Geometry - Quadrilaterals

### Concept

- Quadrilaterals are 4 sided shapes in two dimensions.
- They comes in different shapes based on length of sides, number of parallel sides and lines of symmetry.

### Theory

In order to understand quadrilaterals, it is important to understand the concept of a line, and parallel lines.

##### Lines

Take two points. Join them. Voila - you have a line!

##### Parallel and Intersecting Lines

Draw two lines side by side. If you draw them perfectly side by side, they are parallel lines. If you drew them in a kludge manner (you did, didn’t you?!) then they are intersecting lines.

Parallel lines and intersecting lines are everywhere around us. We give them names so we can talk about them.

##### Quadrilaterals

“Quad” means four and “lateral” means side. So a quadrilateral is just a two-dimensional shape with exactly four sides.

You can classify all the different quadrilaterals using the following properties:

- Side Length
- Parallel (or not)
- Angles made inside the quadrilateral.
- Lines of symmetry, i.e how many ways can you fold the shape into two equal parts.

Let’s start with the **square**.

- Side Length: All sides equal.
- Parallel: Opposite sides are parallel.
- Angle: All angles are 90 degrees.
- Lines of symmetry: 4

A **rectangle**

- Side Length: Only opposite sides are equal, adjacent sides NOT equal.
- Parallel: Opposite sides are parallel.
- Angle: All angles are 90 degrees.
- Lines of symmetry: 2

A **parallelogram**

- Side Length: Only opposite sides equal.
- Parallel: Opposite parallels equal.
- Angle: Can be anything.
- Lines of symmetry: Zip. Nada. Zilch. Try folding it.

Now on to some more exotic quadrilaterals.

A **rhombus** is (very similar to a parallelogram)

- Side Length: All sides are equal
- Parallel: Opposite sides are parallel
- Angle: Can be anything.
- Lines of symmetry: 2

A **trapezium**

- Side length: Can be all different…
- But if the non-parallel sides are equal in length it is an
**isosceles trapezium**

- But if the non-parallel sides are equal in length it is an
- Parallel: Only one pair of parallel lines
- Angle: Anything
- Lines of symmetry: 0 in general, but if it’s an isosceles trapezium, there is one line of symmetry.

A **kite**

- Side length: Adjacent sides are equal.
- Parallel: No parallel lines
- Angle: Anything
- Lines of symmetry: 1

### Misconceptions

- TBD