# Special Right Triangles – The Foundation of Everything Trig

Well, it's that time of the year! As you know your lesson on Special Right Triangles will not only be the foundation for everything trigonometry moving forward but it's also something that their Algebra 2, Pre-Calculus, and Calculus teachers are heavily relying on you to teach them. Teaching the Unit Circle is hard enough if they haven't mastered the Special Right Triangles it becomes a nightmare!

## Special Right Triangles Worksheet and Guided Notes

Below are a Worksheet and Guided Notes to assist you in your lesson but one way I found very effective is to teach them a jingle to remember these few special triangles. They need to be able to create them but they are used so much that needing to memorize them is inevitable. Have them watch the video lesson on their own and then play the jingle throughout class over and over. They will learn the jingle whether they want to or not! Then watch their test scores and recall go up!

If you want more than just these few free resources join the Geometry Teacher Community. You'll never use a text book again!

## Special Right Triangles Guided Math Notes

A Right-angled triangle (named as right triangle) is a triangle which has one of its angles equal to 90 degrees.

There are properties associated with a right triangle.

• A hypotenuse is the line segment opposite to the right-angle.
• An opposite is the line segment opposite to the angle Θ.
• An adjacent is the line segment next to the angle Θ.
• The sum of three angles is 180°i.e. Θ + φ + 90° = 180°

## 45°- 45°- 90° Special Right Triangle

1. 45°-45°-90° triangle

In this triangle, one angle is 90 degrees and other two angles are 45 degrees.

### Properties of a 45°- 45° - 90° Triangle

• Two angles are 45° and one angle is 90°.
• The length of the adjacent and opposite is equal.
• The length of the hypotenuse is √2 × length of leg where leg is the adjacent or opposite.
• A 45°-45°-90° triangle is also termed as an isosceles triangle.

### Sample Problem 1:

What is the length of the hypotenuse of a 45°-45°-90° triangle with leg length √?

By the properties of 45°-45°-90° triangle,

## 30°- 60°- 90° Special Right Triangle

In this triangle, one angle is 90 degrees, one is 30 degrees and one is 60 degrees.

### Properties of a 30°- 60°- 90° Triangle

• One angle is 30°, one angle is 60° and one angle is 90°.
• The length of the adjacent is √3 × opposite.
• The length of the hypotenuse is 2 × opposite.

### Sample Problem 2:

What is the length of the adjacent of a 30°-60°-90° triangle with the opposite length √?

By the properties of 30°-60°-90° triangle,

# Here are some Free Resources for your Special Right Triangles Lesson!

## Word Docs & PowerPoints

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## PDFs

8-2 Bell Work (Members Only)

8-2 Lesson Plan - Special Right Triangles (Members Only)

8-2 Class Activity - Special Right Triangles ( Members Only )

8-2 Online Activities (Members Only)

8-2 Exit Quiz (Members Only)

8-2 Slide Show Presentation (Members Only)

8-2 Video Lesson (Members Only)

## Want Access to the Rest of the Materials for Right Triangles and Trigonometry?

Unit 8 – Right Triangles and Trigonometry

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