2D Shapes and Quadrilaterals

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2D Shapes

A polygon is a shape made up of straight edges.

There are two types of polygons you need to know about:

Regular – All sides and angles are the same
Irregular – All sides and angles are not the same

Regular Polygons

You will already be familiar with the names of some shapes, but it’s important to recognise the names of shapes that have up to $10$ -sides, as seen below.

All the shapes below are regular polygons, meaning all the sides in one shape are the same length.

All of these shapes are regular polygons, meaning that all of their sides are the same length and all the angles are the same.

Irregular polygons

Look at the irregular shapes shown:

Shape A – Counting the number of sides, we see that shape $\textcolor{red}{A}$ has $4$ sides, therefore it is a quadrilateral.

Shape B – Doing the same for $\textcolor{blue}{B}$ , we see that it has $7$ sides, and therefore it is a heptagon.

Quadrilaterals: 6 Common Types

Triangles and quadrilaterals are the shapes we will see most often. As a result, we have names for specific types of them.

The different types of quadrilaterals you should be familiar with are:

1. Square – Has $4$ sides equal in length, and $4$ equal angles (all $90\degree$ ).

2. Rectangle – Has $4$ equal angles (all $90\degree$ ), and its opposite sides are equal in length.

3. Trapezium – Has one pair of parallel sides.

4. Kite – Has two pairs of equal sides, and each pair must be adjacent to each other. Additionally, two of its angles (as marked on the picture) are equal.

5. Parallelogram – Has two pairs of parallel sides. Additionally, opposite angles are equal and adjacent angles add to $180\degree$ .

6. Rhombus – Has $4$ sides equal in length. Additionally, opposite angles are equal, and opposite sides are parallel.

Triangles:

The different types of triangles you should be familiar with are:

1. Equilateral – Has $3$ sides equal in length, and all $3$ angles are $60\degree$ .

2. Isosceles – Has $2$ sides equal in length, and the two base angles are equal.

3. Right-angled – Has $1$ angle equal to $90\degree$ .

4. Scalene – Has $3$ sides of different lengths, and no angles are the same.

2D Shapes and Quadrilaterals Example Questions

Question 1: State the name of the shape below.

[1 mark]

2D Shapes Example Question 1

This shape has 5 sides, so it is an irregular pentagon.

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Question 2: $ABCD$ is a quadrilateral. $AB$ is parallel to $CD$ . State which type of quadrilateral $ABCD$ is.

[1 mark]

2D Shapes Example Question 2

The only feature this quadrilateral has is one pair of parallel sides. Therefore, it must be a trapezium.

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Question 3: $ABCD$ is a parallelogram. Angle $ABC$ is $56\degree$ . Calculate the size of angle $x$ .

[2 marks]

2D Shapes Example Question 3

In a parallelogram, adjacent angles add to $180\degree$ , and angle $x$ is adjacent to ABC, so we get that

$x\degree=180\degree-56\degree=124\degree$

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Specification Points Covered

Geometry and measures – 4. derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language