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May 2013

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The ideas in this geometry lesson are taken from the Geometry ebook that I sell at MathMammoth.com. This lesson plan does not contain all the problems the Geometry ebook does.

Lines, rays, and angles
Free geometry lesson plan from HomeschoolMath.net

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.  Illustrate the same with two pens or pencils.  Move the one pencil while keeping the other stationary, and "see" how the imaginary circle is drawn in the air while you rotate the other pencil.
You can also think of a sun rising in the morning in the horizon, and gradually getting higher, and traveling through the sky along an arc of a circle.  

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.

Example problem types

1.  Which angle is bigger?

a.  OR

b.   OR

2.  Find five objects in your home that have right angles in them.

3.  Mark the angles as acute, right, obtuse, or straight.

[Pictures available in the ebook]

Next geometry lesson