Why are sunbeams called the same as a geometric figure?

Because they start at one point, that is, the sun, and then go on indefinitely. Unless, of course, they hit an obstacle, like you or a tree. Have a look around. There are geometric figures in many everyday things. Rectangles, circles, triangles and also rays and straight lines. But what is the difference between a ray and a straight line?

## Line, segment and ray in geometry – introduction

Even if they are not exactly the same, segment, ray and straight line have one thing in common: they are a straight line.

Take your ruler or set square and draw a line on a piece of paper. That’s a straight line. Or a ray, or a line, depending on how long you draw the line. If the ends go beyond the edge of the paper, it’s a straight line. If it begins on the paper and goes beyond the edge of the paper, if it is a ray and the beginning and end of the line are on the paper, then you have drawn a line. More on the distinction is below.

To better understand straight lines, segments and rays, you should know what a point and a line are.

One point is that **Intersection of two straight lines**** **and describes one **Exact position**. He has **no ****expansion** (Dimension). Several points form one in mathematics **geometric figure**.

No extension means that the point is so small that it practically does not exist. It only exists in our imagination. It is usually shown as a small circle or a cross, but this is only for illustration and is an imaginary indication of position.

One **line **represents one **path** in between **two points**. It arises from the **movement of a point**. Each line is one **infinite set of points**. A line can **just** or **bent** be. In addition, it can have a start and/or end point, but it can also be infinitely long.

This means that each position on a line can be represented by a point. Since this is infinitely small, there are infinitely many points on the line.

## Definition of line, segment and ray

Now we can move on to the straight lines.

### Just

As already mentioned, a straight line is a line that, as the name suggests, is straight.

A straight line is one **line**that on both sides **to infinity** enough. she owns **no start and end point**.

More precisely, a straight line is an infinitely long straight line because it has no beginning and no end.

For example, the axis around which the earth rotates is a straight line, because it is only imaginary and reaches infinitely far into space.

You can find out what you can do with the straight line in the explanation of the straight line.

### half straight

As the name suggests, a ray is half of a straight line.

One **half straight** is the **half of a straight line**. It occurs when a straight line passes through a **Point** is divided into 2 halves. Thus, a ray has one **starting point**but **no endpoint**.

So if you divide a straight line through a point, you get two half-lines that each start at the same point and then go in opposite directions to infinity.

If you draw a number line, you can also see it as a half line, because the 0 separates the positive from the negative numbers. This means that two half-lines begin at point 0 and continue indefinitely.

### beam

You can also find the properties of a half-line in the definition of a ray.

A **beam**** **is a **straight line**that in one **starting point** begins and in a direction in **infinite** goes. A ray has **no endpoint**.

That doesn’t change the fact that it’s still infinite, but at least there’s a point where the ray begins.

You can compare this to the rays of the sun or artificial light, such as a flashlight. The starting point is the light source, i.e. the sun or the light source of the lamp and the beam theoretically shines infinitely far.

In practice, however, light rays are interrupted by dust in the air or obstacles. That’s why you can’t shine a flashlight indefinitely, and there are no longer any sunbeams in the deep sea.

You may have noticed that the ray and ray are very similar. The difference is that a ray never occurs without its counterpart (that is, the other ray with which it shares the starting point), but the ray does.

You can find out how to better distinguish between a half-line and a ray in «Half-line / Ray».

### Route

And finally, the track is missing.

One **Route** is a **straight connection**** two given points**. So she has both **Begin-**as well as one **end point**.

This means that a route is – unlike the previous lines – finite.

People often talk about «route» when it comes to driving a car, for example. Although this route is not completely straight, it usually represents the shortest route. So this route is more colloquial. For example, a mathematically correct route is the trajectory of an airplane because it is not bound by roads and can fly straight to its destination.

## Application of line, segment and ray

Not only is it helpful to know what a line, segment, and ray are, but you can also do something with them. Geometric shapes are used in building and construction.

### parallel straight lines

You need parallel straight lines above all when something is very long and should remain at the same distance.

Parallel lines are two lines that **the same distance at every point** have, meaning they themselves **do not cut**.

In mathematics, the sign **|| **used to describe the parallelism of two straight lines.

Parallel straight lines therefore run infinitely far apart from each other at the same distance.

You can see this, for example, on railway tracks, which usually run very straight and always have to be the same distance apart so that the train can travel on them.

You can find out how to recognize parallel lines and how to draw them yourself in the «Parallel lines» explanation.

### Identical straight lines

In addition to parallel straight lines, there are also congruent straight lines, i.e. straight lines that lie directly on top of each other.

Identical straight lines are a **Special case of parallel lines**. Her **Distance is 0 at every point**. Because of this, they are also called **congruent **designated. So they are actually the same straight lines.

However, you will no longer find identical straight lines in material things, since you can only place them next to each other, but not in the exact same place.

Identical straight lines describe a movement, for example. So it is an imaginary straight line. If a meteorite in space moves on a straight line, i.e. a straight line, and at a different point in time another meteorite takes exactly the same path, then the straight lines that represent their movement are congruent.

Half-lines, rays and lines can also be parallel and identical.

### Lot

If you drop something, it will fall straight down. This is a solder.

A **Lot** is a **Just**the **perpendicular to another line, ray, ray, or segment** stands. So there is a **right angle** at the intersection. This intersection will **nadir point** called.

If you visualize the foot of the plumb, you can immediately notice that it is the point at which the plumb «stands» on the straight line and at the same time that there must be a right angle here, because a foot also has a right angle when standing Has.

You can fell a plummet, but you can also erect it. You can find the difference between felling and erecting in the explanation of the plumb bob.

In everyday life you can always recognize plumb bobs when something is hanging down from above. The surface of the earth is the straight line. The string on which something hangs is the plumb bob. For example, in the case of a crane, the weight always hangs down perpendicularly to the earth’s surface.

## Difference between straight line, segment and ray

Here you will find another overview of how you can distinguish between ray, segment and straight line.

**Just****half straight****beam****Route**

- infinite in both directions
- no start and end point

- infinite in one direction
- Starting point, shares it with the other half of the straight

- infinite in one direction
- starting point

- at last
- start and end point

You can find more about the figures mentioned in the explanations

## Straight, stretch and beam exercises

At the end you can test with a few tasks whether you have understood everything.

**Task 1**

Look at the following picture:

- Which geometric figures can you recognize? (Point P is unimportant for this question)
- What happens if you point P include?

**solution**

- In the picture are one route (blue)one straight (red) and a beam (turquoise) to see.
- point P shares the Just in two half-line as well as the Route into 2 shorter ones stretch.

**exercise 2**

Name the geometric figures in the picture.

**solution**

In the picture, a perpendicular is dropped from a point (e.g. P) onto a line. You can recognize this by the right angle at the intersection. This point of intersection is called the base of the perpendicular.

## Straight line beam – The most important thing

- Straight lines, segments and rays are straight lines. They only differ in their length.
- Lines have no limit and are infinite.
- Half lines are created when a line is divided into two halves by a point. So there are 2 opposing rays that start at the same point.
- Rays have a starting point and go to infinity from there.
- Lines connect 2 points. So you are finite.

- You can often discover straight lines, stretches and rays in everyday life and work with them. They are often divided into the following properties or groups:
- parallel
- identical
- and Lot.

## proof

- Barth, Karl-Heinz; Wulff Heyo; EinFach Mathe. Foundations of Geometry (2000), Schoeningh Verlag
- Henning, Dirk (2012), Math geometry in 15 minutes, DUDEN