A Special Theorem: Part 2 (V3) PBTC
Interact with the applet below for a few minutes. Then answer the questions that follow.
Be sure to alter the locations of points A, B, and C each time before (and even after) you re-slide the slider!
Questions:
1) How would you describe both the blue line p and the green line k with respect to the segment with endpoints A and B? (Hint: Check when slider is half way)
2) Therefore, we can say point D is _______________ from points A and B.
3) C is a point on the blue line p. What can you conclude about the distances AC and BC? (Hint: Finish sliding the slider)
4) Now how would you describe the blue line p? (Hint: This should be different than #1)5) Formally prove, (in the format of a 2-column proof), that your conclusion form #4 is true for any set of points that are equidistant from A and B.
5) Now take a look at the distances FA and FB, when point F is not contained by the blue line p. Notice that these distances are not the same, therefore the green line k is does not form the same special segment as the blue line p.