# Perpendicular Bisector Theorem Converse

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 the

**blue line p**with respect to the

**segment with endpoints**? What exactly is

*A*and*B***line p**? (Hint: It is a special vocabulary term we've already learned! If you're still stumped, consider what the measure of the

**gray angle**. What is it?) 2) Notice how point

*C*always stays on

**line**

**p**. What can you conclude about the

**distances**and

*AC**? 3) Formally prove, (in the format of a 2-column proof, paragraph proof, or coordinate-geometry proof), that your conclusion for (2) is true for*

**BC***any point*

*C*that lies on

**line p**.

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