**Warmup**

**Activity #1**

**Calculate Unknown Side Lengths of a Right Triangle.**

- Label all the hypotenuses with c.

- Find the length of the unknown side.

**Activity #2**

**Calculate Unknown Side Lengths of a Right Triangle.**

- Find the exact value of each variable that represents a side length in a right triangle.

A right triangle has side lengths of a, b, and c units. The longest side has a length of c units.

- Complete each equation to show three relations among a, b, and c.

**Activity #3**

**Find Length of a Line Segment. **

- Use the tools in the applet below to find the length of the line.

(1.) What is the exact length of each line segment? Explain or show your reasoning. (Each grid square represents 1 square unit.)

(2.) What is the exact length of each line segment? Explain or show your reasoning. (Each grid square represents 1 square unit.)

(3.) What is the exact length of each line segment? Explain or show your reasoning. (Each grid square represents 1 square unit.)

**Challenge #1**

Find the value of x in the figure.

**Challenge #2**

The spiral in the figure is made by starting with a right triangle with both legs measuring one unit each. Then a second right triangle is built with one leg measuring one unit, and the other leg being the hypotenuse of the first triangle. A third right triangle is built on the second triangle’s hypotenuse, again with the other leg measuring one unit, and so on.

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