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Another Special Theorem: Part 1 (V3)

Interact with the applet below for a few minutes. Then, answer the questions that follow. Be sure to change the locations of the BLUE POINT and WHITE POINT(S) each time before you re-slide the slider. Be sure to adjust the pink slider as well!
Questions: 1) What can you conclude about the distances from the blue point to each side of the angle? How do you know this? 2) What can you conclude about the location of the blue point with respect to the original (larger) angle? Explain how you know this. 3) Use your observation to fill in the blanks to make a true statement: If a point is _____________________ from the sides of an angle, then that point lies on the  _______________ of that angle. 4) Write a 2-column or paragraph proof that proves the statement in (4) true.