Special Right Triangle (I) - Investigation
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.