# Geometry (Mathematics Curriculum)

# Shapes

## What Is Geometry?

Geometry is a branch mathematics that studies shapes and their properties.

### Dictionary Definition

The Oxford English Dictionary defines geometry as "the branch of mathematics concerned with the properties and relations of points, lines, surfaces, and solids."

Here are some examples of common shapes. We might be interested in finding the angle in a triangle, the area of a circle or the volume of a cone. Geometry allows us to do this.

## Where Does the Word Geometry Come From?

Geometry comes from combining the Greek words 'ge' ("earth") and 'metria' ("measurement").

Geometry means measuring the earth or land. This is because initially geometry would have been used practically to measure areas of fields and the lengths of roads.

## Euclid and Geometry

Euclid was an ancient Greek mathematician, famous for his work in geometry.

His book of geometry, *Elements*, is one of the most widely read books of all time and has earned Euclid the nickname the *Father of Geometry*.

Euclid has had many great fans.

Abraham Lincoln kept a copy of Euclid in his saddlebag and would read it late at night by lamplight to aid his career as a lawyer:

"You never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father's house and stayed there till I could give any proposition in the six books of Euclid at sight".

Albert Einstein received a copy when he was a boy and claimed it had a great influence on him. He called *Elements* the "holy little geometry book".

## Plane Shapes

Plane shapes are two-dimensional, flat shapes: such as circles, squares and triangles.

In this mini-curriculum, you will learn about plane shapes.

## Areas

Area is a measure of the size of a plane shape. Larger shapes have more area.

In this mini-curriculum, you will learn the areas of plane shapes.

## Volumes

Volume is a measure of a space that a three-dimensional shape contains.

In this mini-curriculum, you will learn the volumes of shapes.

## Circles

Circles have an interesting geometry; there are many terms to understand: radius, diameter, circumference, sector and segment.

In this mini-curriculum, you will learn about circle geometry.

## Radius of a Circle

The radius is the line segment from the center of the circle to any point on the circle.

The radius also refers to the length of this line segment.

In this mini-curriculum, you will learn about how to find the length of the radius from the other dimensions of a circle.

## Diameter of a Circle

The diameter is the line segment that contains the centre of the circle and has its endpoints on the circle.

The diameter also refers to the length of this line segment.

In this mini-curriculum, you will learn about how to find the length of the diameter from the other dimensions of a circle.

## Area of a Circle

The area of a circle is can be found from the diameter.

In this mini-curriculum, you will learn about how to find the area of a curcler from its diameter.

## Circle Theorems

Circles have properties related to angles and lines.

In this mini-curriculum, you will learn the circle theorems that relate to all circles, such as that tangents meet the radius at 90° and the alternate segment theorem.

## Triangles

A triangle is a shape with three sides and three angles.

In this mini-curriculum, you will learn about the different types of triangles and their properties.

## Angles

An angle is a created when two lines meet. It is also a measure of the rotation between the two lines.

In this mini-curriculum, you will learn about the different types of angles and how they are measured.

## Angle Properties

Two more angles can add up to a right angle, a straight angle or a full angle.

In this mini-curriculum, you will learn about complementary angles, supplementary angles and explementary angles.

## Polygons

A polygon is a 2-dimensional shape with straight sides.

In this mini-curriculum, you will learn about different types of polygons and their properties.