[color=#000000]In the applet below, [/color][color=#1e84cc][b]line p[/b][/color][color=#000000] is the [/color][color=#1e84cc][b]perpendicular bisector[/b][/color][color=#000000] of the [/color][b]segment with endpoints [i]A[/i] and [i]B[/i][/b][color=#000000]. [br][br]If you forgot what it means for a line to be a [/color][color=#1e84cc][b]perpendicular bisector[/b][/color][color=#000000] of a [/color][b]segment[/b][color=#000000],[br][/color][color=#000000]you can slide the slider on the left for a reminder. You can also revisit [/color][url=https://tube.geogebra.org/m/pznR4BnT]this worksheet[/url]. [br][br][color=#000000]The slider on the right gives insight into a theorem that holds true for every point that lies on the [br][/color][color=#1e84cc][b]perpendicular bisector[/b][/color][color=#000000] of a [/color][b]segment[/b][color=#000000]. [br][br][/color][color=#000000]Interact with this applet for a few minutes. [i]As you do, be sure to change the location of the white point C each time before you re-slide the slider. [/i][br][br]Answer the questions that follow. [/color]

[color=#000000][b]Questions: [/b][/color][br][br][color=#000000]1) What do you notice about the distances (lengths) [/color][i][color=#ff00ff][b]AC[/b][/color][/i] [color=#000000]and[/color] [i][color=#ff00ff][b]BC[/b][/color][/i]? [br][br][color=#000000]2) Does your answer to question (1) above hold true for [i]every point[/i] on this[/color] [color=#1e84cc][b]perpendicular bisector[/b][/color]? [br] [color=#000000] That is, is your response to question (1) the same regardless of where point [i]C[/i] lies? [/color][br][br][color=#000000]3) If your answer to (2) was [b]yes[/b], prove this assertion true in the format of a 2-column proof. [/color]