[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]. [/color][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][/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? [br][br][/color]3) Let D be the point where segment AB intersects line p. Using similar triangles, which triangle cases proves that triangle ACD is congruent to triangle BCD?[br][br][color=#000000]4) Prove this assertion (2 and 3) true in the format of a 2-column proof. [/color]