# Special Right Triangle (I) - Investigation

- Author:
- Leigh Paris Haywood, Tim Brzezinski

## 1.

How would you classify the triangle above *by its sides? *

## 2.

What is the measure of the **gray angle**? Explain how you know this to be true.

## 3.

What is the measure of each acute pink angle? Explain how you know this to be true.

## 4.

What are the measures of this triangle's interior angles? (List from least to greatest.)

## 5.

Suppose the **thick black segment** in the triangle above **measures 3 inches. **
Algebraically determine the length of the longest side of this triangle in simple radical form.

## 6.

Suppose the **thick black segment** in the triangle above **measures 4 inches. **
Algebraically determine the length of the longest side of this triangle in simple radical form.

## 7.

Suppose the **thick black segment** in the triangle above **measures 5 inches. **
Algebraically determine the length of the longest side of this triangle in simple radical form.

## 8.

Suppose the **thick black segment** in the triangle above **measures 6 inches. **
Algebraically determine the length of the longest side of this triangle in simple radical form.

## 9.

Do you notice any patterns in your answers for questions (5) - (8) above? Explain.

## 10.

Suppose we call **thick black segment** in the triangle above as * LEG. *
What would the length of this triangle's longest side be (in terms of

**?)**

*"LEG"*## 11.

Algebraically prove your response to (10) true.