# Special Right Triangle (I) 45-45-90

Interact with the applet below for a few minutes, and then answer the questions that follow.

**Questions:**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) Same as question (6), this time for the length of the thick black segment measuring 5 inches. 8) Same as question (6), this time for the length of the thick black segment measuring 6 inches. 9) Do you notice any patterns in your answers for questions (5) - (8) above? Explain. 10) Suppose the thick black segment in the triangle above has length

*a*. What would the length of this triangle's longest side be in simple radical form? 11) Prove your response to (10) true.

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