Lines, rays, and angles

A line has no beginning point or end point. Imagine it continuing indefinitely to both directions. We can illustrate that by little arrows on both ends.

A line segment has a beginning point and an end point.

All the sides of this triangle

are line segments.

A ray has a beginning point but no end point. Think of sun’s rays: they start at sun and go on forever…

What is an angle? Many people think that angle is some kind of slanted line. But in mathematics an angle is made up from two rays that have the same beginning point. That point is called the vertex and the two rays are called the sides of the angle.

You can think of the two sides of the angle as having started side by side, and having opened up to a certain point. When the two sides “open up”, they draw an imaginary arc of a circle. Look at the pictures.

This angle is called the zero angle. In each picture the angle keeps getting bigger. The arc of the circle is larger. The angle is opened more and more. These angles are acute angles, which means they are less than a right angle. Think of the acute angles as sharp angles. If someone stabbed you with the vertex of the angle, it would be sharp.

This angle is called

the right angle.

For example, table corners are right angles. The angle is opened even more and is bigger than the right angle. It is an obtuse angle. Obtuse angles are dull angles. This angle is called the straight angle.

It does not matter how long the sides of the angle appear. Remember, they are rays, and rays don’t have an endpoint, but when drawn on paper, they do end somewhere. The sides of the angle might even seem to have different length. That doesn’t matter either. The size of the angle is ONLY determined by how much it has “opened”, or how big part of a arc of a circle the sides have drawn.

Which of these two angles is bigger?

Remember to look at how much

the angle has opened, or how big

part of a circle the sides have drawn.

Many times the arrows are omitted

from the rays, and the arc of the circle

is drawn as a very tiny arc near the vertex:

Even the little arc is not necessary.