# Geometry

Geometry is a part of mathematics that ** deals with **forms, ** shapes **and the ** sizes **of objects. There are many different kinds of ** shapes **. Some are two-dimensional like circles, ** squares **or ** triangles**, others are three-dimensional like ** cubes**, balls or ** cones **. Geometry shows us how we can construct or draw such forms and how to ** measure **them.

We need geometry in everyday life . Houses are made up of geometrical ** shapes**. Pilots use geometry when they plan their routes and ** surveyors **need geometry to make maps and ** measure areas **of land.

The world is full of geometric ** shapes**. Egyptian pyramids got their name from geometry and the biggest building in Washington is the Pentagon, a ** structure **that has five sides.

### Plane Figures and Shapes

A ** plane **is a flat ** surface **like the top of a table. ** Plane **geometry is also called two-dimensional geometry.

#### Lines and Angles

The simplest objects in geometry are lines and ** angles**. A line is straight and has two ** arrowheads **which show that it ** continues **in both directions. A ** ray **is a line that has a starting point and then goes on in a ** certain **direction. Two lines that come together and have the same starting point form an ** angle **. It can be ** measured **in ** degrees**.

** Angles ** that make ** square **corners ** measure **90° and are called right angles. Angles with less than 90° are ** acute**, those with more than 90° are called ** obtuse**. Two lines that never meet are parallel.

#### Polygons

When several ** segments **of a line ** join **together they create a ** closed **figure called a polygon.

#### Triangles

A polygon with three sides is a ** triangle**. If all three sides have the same ** length **we have an ** equilateral** triangle, two sides of the same length make up an ** isosceles **triangle. A triangle with one right angle is called a right triangle. The side ** opposite **the right angle is the hypotenuse , the other two sides are called ** legs**.

The Greek mathematician Pythagoras , who lived at about 500 B.C. ,found out that there is a ** connection **between the length of the ** legs **and the hypotenuse of a right triangle. If you add up the squares of both ** legs **it is ** equal **to the square of the hypotenuse.

#### Quadrilaterals

** **

**Quadrilaterals ** are polygons with four sides. They have many more shapes than ** triangles **do.

A ** quadrilateral **with four right ** angles **is a rectangle. If all sides of this rectangle have the same ** length **we call it a square. A parallelogram has ** opposite **sides that are parallel and ** equal **in ** length**. If all sides are the same in ** length **we call it a rhombus.

#### Other polygons

The term polygon comes from the Greek language and means "many ** angles**". A five-sided polygon is a pentagon. Hexagons (six sides) are shapes we use to ** tile **floors or bees use for their ** honeycombs**. The stop sign we see at a road ** crossing **is an eight-sided polygon , an octagon.

#### Circle

** Shapes ** are not always made up of straight lines. A circle is a curved line. All points on this line have the same ** distance **from the centre. Circles are found everywhere in our daily life—wheels, ** coins **and cups have ** circular shapes**.

The line that cuts the circle into two ** equal **halves is called the ** diameter**. The radius is the line from the centre of the circle to every point on its ** border**.

### Solids

** **

**Solids ** are three-dimensional objects. They have a ** length**, ** width **and a ** height**.

A ** polyhedron **is a figure with ** flat **faces and straight ** edges**. A ** cube**, for example, is built from a square. It has six ** faces **that are all the same. However, not all ** polyhedrons **are regular. A ** prism **has two parallel ** bases** and its other faces are parallelograms . A pyramid has a ** base** that has four sides , the other ** faces **are ** triangles**.

Some solids are curved. A ** sphere **is a ball-shaped object with a completely round ** surface**. The distance from the middle to every point on the ** surface **of the ** sphere **is always the same.

Cylinders are ** shapes **that we find in cans or ** pipes**. They have two circles as ** bases **and a curved side. The ** cone **is probably the most ** familiar **too us because it is ** shaped **like an ice cream.

### Measuring geometrical objects

The ** area **is the ** surface **that a figure ** covers**. It can be ** measured **by putting squares on a shape and then counting them . A ** rectangle **with a ** length **of 5 cm and a ** width **of 4 cm has an ** area **of 20 square centimeters. You can put 20 square centimeter ** units **into it.

** Measuring ** the ** area **of other objects may be more difficult. You can get a ** triangle's area **by multiplying the ** base line **with its ** height **and then dividing it by two.

The ** area **of a circle is the ** square **of the radius multiplied by 3.14159 , a constant called Pi.

The amount of ** space **that a ** solid **figure fills is called its ** volume**. ** Basically**, you can get the volume when you multiplying the ** area **of the base by the ** height **of the object. The unit for volume is the ** cube **. A box, for example that has a ** length**, ** width **and ** height **of 1 m would have a ** volume **of 1 cubic metre.

The ** volume **of curved or ** irregular **objects are much more difficult to ** calculate**. Mathematicians have complex ** formulas **for finding out the ** volume **of a ** sphere **or a ** cone**.

### Downloadable PDF Text- and Worksheets

### Words

**acute**= an angle of less than 90°**angle**= the space between two lines that join each other**area**= the space that a shape covers**arrowhead**=the sharp, pointed end of an arrow**base**=bottom**base line**=here: the line at the bottom**basically**=on the whole, normally**border**=end, margin**calculate**= to work out the size, length, volume etc... of something**certain**=special**circular**= the form and shape of a circle**closed**=not open**coin**= a round flat piece of metal that is used for money**cone**= an object that is round at one end and pointed at the other**connection**=link, relationship**continue**= go on**cover**=spread over**crossing**=where two or more roads meet**cube**= an object with six equal sides**deal with**= is about**degree**= unit for measuring the size of an angle**diameter**= a straight line from one side of a circle to the other; it passes through the centre of the circle**distance**=space between two things**equal**= the same**equilateral**= all sides are the same**face**= part of the outside surface**familiar**= well known**formula**=numbers that form an equation or a mathematical rule**height**=how high something is**honeycomb**= a structure made by bees. It is made up of six-sides cells in which bees put their honey**irregular**= a shape that is not smooth or even**isosceles**= two of the three sides have the same length**join**= get together, meet**leg**=side**length**=how longs something is**measure**=to find out how big, long or heavy something is**obtuse**= an angle of more than 90°**opposite**= on the other side of**pipe**= a tube through which water or other things can flow**plane**=a completely flat surface**polyhedron**= a solid shape with many sides**prism**=an object that has the same ends and sides that go up**quadrilateral**= a flat shape with four straight sides**ray**=a line that goes in a certain direction**rectangle**= a shape that has four straight sides and four 90° angles**segment**= part of a line**shape**= the form that something has**size**= how big or how small something is**solid**= hard, with a fixed shape**space**=room, area**sphere**= a ball shape**square**=a shape with four equal sides and right angles**structure**= building**surface**=the top part of something**surveyor**= a person who measures land**tile**= to cover a floor with small plates**triangle**= a flat shape with three sides and three angles**unit**=an amount of something that is used to measure**volume**=the amount that an object or container fills**width**=how wide something is