# Special Right Triangle (I)

Interact with the applet below for a few minutes. As you do, be sure to change the locations of the LARGE WHITE POINTS each time before re-sliding the slider. Then, answer the questions that follow.

## 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"?)