Technicalities of Lines, Rays, and Line Segments

Some algebra and geometry teachers can be real sticklers when it comes to these three models. There are slight differences between the three and I'm going to help you separate them.

A Line Segment  has two define endpoints, which is how it is labeled, and has no arrows as follows:

Line segment AB:



A Line is like a line segment, in which it is identified by two points. The line however continues on in both directions, so the ends are marked with arrows:

Line AB and Line GH:


A Ray is a nice healthy mix of the two. One end ends in a point, while the other has an arrow. A Ray also is identified by two points:

Ray AB:


Any Questions? Please, comment. I am more than willing to help you with anything you need. :)

Special Right Triangles: 30-60-90

Special Right Triangles again? you might ask. Indeed there is more. This type of Special Right Triangle is called the 30-60-90. This is because it contains one 30 degree angle, one 60 degree angle, and one 90 degree angle. Solving these is fairly similar to the 45-45-90 triangles. Here is an example:

The short leg, 'x', is always opposite the 30 degree angle. The hypotenuse, is always exactly 2 * 'x', and it will always be opposite the 90 degree angle. And lastly, we have the long leg, always opposite 60, and is 'x' times the square root of 3.

In this example, we are going to solve for 'x' and 'y'.

First, we are going to solve for the short leg which in this case, is 'x'.

Since we know that 4 square roots 3 = 'x' square root of three,  we know that 'x' is equal to 4. This is because to get 'x' by itself, we need to divide both sides by the square root of 3. The equation would then be set to x = 4.

Now, to solve for 'y' all we have to do is double the short leg. Since we now know the short leg is 4, we know that y = 8.

And that is all you have to do to solve 30-60-90 triangles!! 

As always, if you are even a little bit confused, comment!