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
- 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