# Special Right Triangles Geometry Worksheets

Special right triangles are those triangles that fit an exact ratio by the means of angle measures. All the measures of this shape fit nice and neat into the use of the Pythagorean Theorem (a^{2} + b^{2} = c^{2}). This makes them super easy to work with and once you know a single measure, you know pretty much everything about its dimensions and measures. This selection of worksheets and lessons shows students how to manipulate special right triangles to your advantage in many situations.

### Aligned Standard: HSF-TF.A.3

- Find A Leg Step-by-Step Lesson- When you compare attacking these problems from a Trigonometric or Geometric view; my old professor would say the Geometric views were the way god intended it to be solved.
- Guided Lesson - One triangle with three missing parts. Get to work!
- Guided Lesson Explanation - This one should fly by at this level. This is noting more than a warm-up, at best.
- Practice Worksheet - I have no idea why I didn't just work off of one triangle, but I didn't.
- Matching Worksheet - Find those missing values and make them plug the holes in the triangles.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

The main purpose over the course of these homework sheets is to help students get more comfortable manipulating triangle measures..

- Homework 1 - We are concerned with determining the length of sides here.
- Homework 2 - This one is focused on the measures of missing angles.

### Practice Worksheets

If you have trouble here, refer back to the lesson and see how it goes.

- Practice 1 - We are not focused on the ratio method here.
- Practice 2 - This is a complete review for you on this skill.

### Math Skill Quiz

This single quiz does a nice job of seeing where you are at with this skill.

- Quiz - We will see how you are at finding both unknown measures of angles and length of sides.

### What are Special Right Triangles?

When you are learning geometry, right triangles are the core shape which you need to know. Especially because the Pythagoras theorem is one of the most used formulae in this branch of mathematics. That is because you need very little information to determine all of the measures and dimensions of them. These are triangles that possess a ninety-degree angle. Because the internal angles of triangle have a sum of one-hundred and eighty degrees that means the sum of the remaining unknown internal angles of a right triangle must be ninety degrees as well. However, the other two angles can be of any value.

Special right triangles are right triangles that have very simple ratios between the lengths of their sides. This makes them simple to determine the value of missing measures with. The most commonly used are 45-45-90 and 30-60-90 forms. Those value indicate the measure of their internal angles. Each of these types has a specific ratio which means if we know the measure of a single internal angle, we can calculate all the others by simplify applying the ratios to it. If you can find right triangles that match these angle measures, you can quickly calculate just about everything about them. This also helps us classify the type of triangle that is at work here.