# 2D shapes

2D stands for *two-dimensional*. 2D shapes
are ‘flat’ shapes – they are shapes you can cut out of a flat sheet of paper.
A page of this book is an example of a 2D shape – it is a rectangle.

These are some examples of two-dimensional shapes:

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2D shapes are often called *plane shapes*.
The ‘plane’ part is to do with how you can represent these shapes using a *plane*
– which is a flat area. For example, you can make a rectangle out of a piece
of paper by cutting it out. But if you wanted to make a cube, you’d have to
fold the paper and make a *solid* shape. It would no longer be a plane
shape.

### Quadrilaterals

*Quadrilaterals* are shapes with exactly *four*
straight sides. They also have exactly *four* corners. *The interior
angles of any quadrilateral add up to 360°*. There are lots of special
types of quadrilaterals – here are some of them:

### Parallelograms

A *parallelogram* is a quadrilateral – it has
four sides and four corners. However, it also has some special characteristics.
Each pair of opposite sides is *parallel* to each other. Here’s a typical
parallelogram:

Notice that each side is parallel with the side *opposite*
it. Also, the lengths of opposite sides in a parallelogram are the same.

### The rectangle

A *rectangle* is a type of parallelogram, with
*all* the interior angles exactly 90°.

### The square

A *square* is an even more specialised type of
parallelogram than the rectangle. A square has all the properties of a rectangle,
but on top of these, *all* the sides of a square are the same length:

### The rhombus

A *rhombus* is like a square except that the
interior angles can be any value at all, not just 90°. The square is a special
type of rhombus.

Find a: |

Solution |

Sometimes these problems can be done quite quickly, if you keep an eye out for symmetrical or identical looking parts of the diagram. In this case, if you look more closely at the circled regions in the diagram, and extend a couple of the lines a little bit, you’ll see they’re identical: Since these two areas are identical in their
layout, all we need to do is find an appropriate rule that uses the 132° to
work out what ‘a’ is. In this case, we have two straight lines crossing or
intersecting each other. ‘a’ and the 132° are In this case we know that the two areas of the
diagram are identical because the |

### Closed shapes

A closed shape is one that doesn’t have any gaps in its border. A square or rectangle is a closed shape because you can start at a point on the border, and follow it around until you get back to where you started, without having to reverse direction. But if you had a shape which looked like a ‘C’, if you started at one point and kept moving, you’d have to eventually reverse direction to get back to where you started. It would not be a closed shape.

So a shape like this is a *closed* shape
because you can always get back to where you started on the border, *without
having to reverse* direction. You do *change* direction at the
corners, which is OK, but you never have to stop and go back the way you came.
But if you have a shape like this, you have to actually reverse direction: