Special Right Triangle (I)
[color=#000000]Interact with the applet below for a few minutes. [br][br]As you do, be sure to change the locations of the LARGE WHITE POINTS each time before re-sliding the slider. [br][br]Then, answer the questions that follow. [/color]
1.
How would you classify the triangle above [i]by its sides? [/i]
2.
[color=#000000]What is the measure of the [/color][b][color=#666666]gray angle[/color][/b]? [color=#000000]Explain how you know this to be true. [br][/color][color=#000000][br][/color]
3.
[color=#000000]What is the measure of each[/color] [color=#ff00ff]acute pink angle[/color]? [color=#000000]Explain how you know this to be true. [br][/color][color=#000000][br][/color]
4.
What are the measures of this triangle's interior angles? (List from least to greatest.) [br]
5.
Suppose the [b]thick black segment[/b] in the triangle above [b]measures 3 inches. [/b][br]Algebraically determine the length of the longest side of this triangle in simple radical form.
6.
Suppose the [b]thick black segment[/b] in the triangle above [b]measures 4 inches. [/b][br]Algebraically determine the length of the longest side of this triangle in simple radical form.
7.
Suppose the [b]thick black segment[/b] in the triangle above [b]measures 5 inches. [/b][br]Algebraically determine the length of the longest side of this triangle in simple radical form.
8.
Suppose the [b]thick black segment[/b] in the triangle above [b]measures 6 inches. [/b][br]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 [b]thick black segment[/b] in the triangle above as [i][b]LEG. [/b][/i][br]What would the length of this triangle's longest side be (in terms of [b][i]"LEG"[/i][/b]?)
11.
Algebraically prove your response to (10) true.