Special Right Triangles Worksheets

Free Worksheets for Special Right Triangles with Complete Answer Keys

If you’re in need of a practice worksheet for special right triangles with a complete answer key, then check out our free Special Right Triangles Worksheets Library, where you can download several PDF practice worksheets to use at home or in the classroom.

In the section below, you will find a free collection of printable special right triangles worksheets that can be downloaded as printable PDF files. Each special right triangles worksheet includes a reference box at the top of the page along with ten different practice problems. The worksheets include space to show your work as well as a complete answer key so you can check your progress as you go.

If you are struggling to solve the problems on any special right triangle worksheet, you can visit the second section of this guide for a quick recap/review of special right triangles and how to solve problems involving them.

You can preview any worksheet for special right triangles by click on any of the image links below, and can download the corresponding PDF file by clicking on any of the blue text links. Once you click on any of the blue text links, you will be able to save the PDF file to your device or send it to your printer.

The free special right triangles worksheets available in the library below are samples from the Mashup Math K-12 Infinite Worksheet Libraries available on our website. | Reference: How to Download/Print

Special Right Triangles Worksheets

▶️ Practice with Special Right Triangles (A)

▶️ Practice with Special Right Triangles (B)

▶️ Practice with Special Right Triangles (C)

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Special Right Triangles Worksheet Review

If you are having a hard time with struggling to solve any of the problems on a worksheet for special right triangles above, then continue forward with this short review of special right triangles and how to understand them.

The first important thing about special right triangles to understand is that there are two types of special right triangles:

• 45-45-90-degree right triangle

• 30-60-90 degree right triangle

Whenever a right triangle falls into one of these categories, it is considered a special right triangle whose side lengths (the shorter leg, the longer leg, and the hypotenuse) have a proportional relationship.

Namely, these angle relationships

• 45-45-90 right triangle has side lengths of x, x, and x√2

• 30-60-90 right triangle has side lengths of x, x√3, and 2x

In order to solve the problems on our special right triangles worksheets, you have to be familiar with these relationships.

For example, let’s say that you are given a right triangle with angle measures 45-45-90 where one of the lengths of the legs is 8 units. How would you find the lengths of the other leg and the length of the hypotenuse?

Since the given right triangle has angle measures of 45-45-90, then we know that it is a special right triangle.

This means that we can use the fact that 45-45-90 right triangles have side lengths of x, x, and x√2 where x√2 is the hypotenuse. So, in this example, the given side length of 8 represents x, which means that both of the legs have lengths of x, and the hypotenuse, x√2, can be expressed as 8√2 .

Again, this x, x, and x√2 relationship applies to all 45-45-90 right triangles.

For another example, consider a 30-60-90 right triangle where the shortest leg has a measure of 3 units.

Since this given right triangle has angle measures of 30-60-90, it falls into the category of being a special right triangle.

This means that we can use the fact that 30-60-90 right triangles have side lengths of x, x√3, and 2x is the hypotenuse. So, in this example, the given length of 3 is the shortest side. In this case, the shortest side is represented by x, so we can say that:

• x → 3

• x√3 → 3√3

• 2x → 2(3) = 6

So, we can now say that this right triangle has length with lengths of 3 and 3√3 and a hypotenuse length of 6.