# A Special Theorem: Part 2 (V2)

In the applet below,

**line p**is the**perpendicular bisector**of the**segment with endpoints**. If you forgot what it means for a line to be a*A*and*B***perpendicular bisector**of a**segment**, you can slide the slider on the left for a reminder. You can also revisit this worksheet. The slider on the right gives insight into a theorem that holds true for every point that lies on the**perpendicular bisector**of a**segment**. Interact with this applet for a few minutes.*As you do, be sure to change the location of the white point C each time before you re-slide the slider.*Answer the questions that follow.**Questions:**1) What do you notice about the distances (lengths)

*and*

**AC***? 2) Does your answer to question (1) above hold true for*

**BC***every point*on this

**perpendicular bisector**? That is, is your response to question (1) the same regardless of where point

*C*lies? 3) If your answer to (2) was

**yes**, prove this assertion true in the format of a 2-column proof.

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