# Geomentry

### Math With Shapes

Throughout this "Presentation" I am going to show you how to do the "30-60-90" and "45-45-90" Triangles. I'm going to give you examples and links that you can go to that will probably give you a better explanation than what I am going to be doing. Also throughout this "Presentation" I am going to show you how to tell weather or not Triangles are Simlar.

**30-60-90 Triangles**

Below is a youtube video that you can watch that will show you how to do 30-36-90 Triangles:

Just in Case the Video does not work I am going to explain this way..........

Your Longest Side of your Triangle is called the "Hypotenuse". Your other two side of the triangle are called the "Legs".

Looking at your Triangle: The Right Side of the Triangle where R & M are, your going to have some kind of number there. For this example that number is going to be 5. If you look at your Hypotenuse, you notice that that side has a 10. See all you do is add 5 to your other 5 which equals 10. Now on the other side you are going to have a Square Root Sign with the number 3 in side of it. On 30-60-90 Triangles that number inside of your square root is always going to be the number 3. If you look at the right side of the triangle again, your side with the square root sign will have a 5 out beside it. I know this is confusing. The number 5 beside the square root sign with the 3 inside of it, comes from the side of your triangle that already has a 5 beside it.

# 45-45-90 Triangles

Like I said before just in case the video does not work I am going to explain how to do the "45-45-90" Triangle system below:

45-45-90 Triangles

Looking at your Triangle: Instead of the number being 3 inside of your square root, its going to be 2. ONLY FOR 45-45-90 TRIANGLES ONLY. Looking at Triangle: Your hypotenuse is 6. What plus what equals 6? 3 Of course so your other two sides should be 3 with the square root sign with the number 2 inside of it. Sorry if I am confusing you. Hopefully the video works for you and its explains this better. You get the point.

# How do you tell weather or not Two Triangle Similar? Hmm..........

Here is an example that I did in Math Class:

Looking at the example you notice a big Triangle and a Smaller Triangle....A New one and an Old one. The New one is on the left and the Old one of the right. Your looking for your scale factor. You take the top number of your New Triangle and the top number from the Old Triangle and you turn them into a Fraction which would be 3/1 (Three over One) You do the same for the other sides of both of the Triangles....You take your 6 from the New Triangle and Match it with the 2 from the other triangle which are on same sides of both triangles and you turn them two into a fraction which would be 6/2 (Six over Two) You then ask yourself what can both 3 and one be divided into....Which is the Number 3. You then look at your other fraction and ask the same question..What can both 6 and 2 be divided into..Which is the number 3. You got the number 3 for both Triangles which then means, YOUR TRIANGLES ARE SIMILAR. If you repeat these steps with another example and you don't get the same number for both fractions then the equations is NOT SIMILAR! Therefore your scale factor is 3.