Geometry

We will start with a point.

A point is one of the basic terms in geometry.

A point is a single location in space. A point has neither length nor width. It simply specifies an exact location.

Nevertheless, we may think of a point as a "dot" on a piece of paper.

We usually identify points with a capital letter. The following is a diagram of point Q:

Geometry

Fourth Grade Geometry

Geometry is a fun mathematics topic because you get to draw lots of cool lines and shapes!

Not only that, but you can really "see" what you're learning, which makes it easier to understand than a lot of "abstract" ideas that you have to imagine.

What you are about to look at is a handy reference guide for geometry topics complete with examples, definitions, and explanations.

It follows a logical order beginning with points.

Okay now, let's go!

EXAMPLE

That's the way we draw it. The way we say it is . . .

"Point Q."

I bet you wonder from where we got the letter "Q."

Actually, we chose it at random. We could have choosen any letter we wanted. We could have chosen H, or P, or X, but we chose Q. It was totally up to us.

If a point doesn't already have a name, you can name it with ANY letter you wish (as long as you haven't already given that name away to another point on the same page). Cool, huh?

Now lets look at lines.

A line is another of the basic terms in geometry.

A line is a series of points, which form a straight path that goes on forever and ever in both directions.

We may think of a line as a long, straight mark drawn with a ruler on a piece of paper, except that in geometry, lines NEVER stop!

We name a line by identifying two points lying upon it.

For example, this is a diagram of line EF . . .

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EXAMPLE

Now lets look at rays.

A ray is a series of points that form a straght path starting at a particular spot and going on forever in one direction.

The point where the ray begins is known as its endpoint.

Now lets look at line segments.

We may think of a line segment as a "straight" mark that begins at a particular point and also ends at a aspecific point.

The points where the line segment begins and ends are known as its endpoints.

FOURTH GRADE GEOMETRY

Geometry

FOURTH GRADE GEOMETRY

Example: The opposite sides of the rectangle below are parallel. The lines passing through them never meet.

Parallel Lines

Two lines in the same plane which never intersect are called parallel lines. We say that two line segments are parallel if the lines that they lie on are parallel. If line 1 is parallel to line 2, we write it like this . . .

line 1 || line 2

When two line segments DC and AB lie on parallel lines, we write it like this . . .

segment DC || segment AB.

Example: Lines 1 and 2 below are parallel.

Geometry

Intersecting Lines

The term intersect is used when lines, rays, line segments or figures touch, that is, they share a common point. The point where they meet is called

the point of intersection. We say that these figures intersect.

Example: In the diagram below, line AB and line GH intersect at point D:

Example: In the diagram below, line 1 intersects the square in points M and N.

(Note also that each of the

corners of the square are

formed by two intesecting

line segments as well.)

Geometry

Polygons

A polygon is a closed plane (flat) figure (shape) made by joining three or more line segments. (In other words, each line segment intersects exactly two others.)

Examples:

The following are examples of polygons . . .

Triangles

A three-sided polygon.

Examples:

isosceles trinagle: A triangle having two sides of equal length.

equilateral trinagle: triangle having all three sides of equal length. The angles of an equilateral triangle all measure 60 degrees.

EXAMPLES:

EXAMPLES

scalene trinagle: A triangle having three sides of different lengths.

acute trinagle: a triangle having three acute angles.

EXAMPLES:

obtuse trinagle: A triangle having an obtuse angle. One of the angles of the triangle measures more than 90 degrees.

EXAMPLES:

right trinagle: A triangle having an obtuse angle. One of the angles of the triangle measures more than 90 degrees.

EXAMPLES:

Perpendicular Lines

The term perpendicular is used when lines, rays, line segments or figures meet, to form a shape that is like a capital L. That is to say, they form a 90º angle.

Another way to describe perpendicular lines, rays, or line segements is to say that they form a "square corner."

To test whether or not two lines, rays, or line segments are perpendicular, simply place the corner of a standard 8.5 x 11 sheet of paper where they form a vertex and see if they line up with the sides of the paper. Below are examples of perpendicular lines, rays, and line segments.

This is the sign of a

90º degree angle.

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Geometry

T S

We write the name of a ray with endpoint M and passing through a point N as MN.

You need to know the endpoint is always listed first, no matter in which direction the ray actually extends. So, even if the ray points to the left, it is still written with the arrow head pointing to the right.

In other words, regardless of which direction the arrow is pointing, when writing a ray, we ALWAYS write the endpoint first, whether it is was located on the right side of the ray or on the left.

Example: The following is a diagram of ray ST.

That's the way we draw it. We write it like this: ST

And again, we can choose any two letters we want to name our ray, just as we did with our line.

We draw it like that, but we write it like this: EF

Notice the two-headed arrow over EF signifying a line passing through points E and F.

And we say, "Line EF."

(Since we can't really draw lines that go on forever and ever, we place an arrow at each end to signify that the line never stops.)

We write the name of a line segment with endpoints M and N like this: MN. As with lines, the direction doesn't matter, so we could also write it like this: NM

Example: We say: "line segment NM." Here is its diagram . . .