[size=150]In the applet below, the constructed [b][color=#0000ff]perpendicular bisector[/color][/b] of [b][color=#666666]segment [i]AB[/i][/color][/b] is shown. [br][br]Add a point [i]C[/i] on the perpendicular bisector.[br]Join [i]A[/i] to [i]C [/i]and [i]B[/i] to [i]C [/i]to form a triangle [i]ABC.[br][br][/i]Compare the lengths [i]AC[/i] and [i]BC[/i] .[br]Move [color=#9900ff][b]point [/b][/color][i][color=#9900ff][b]C[/b][/color] [/i]along the [color=#0000ff]perpendicular bisector[/color] (anywhere above or below [b]segment [i]AB[/i][/b])[br]Again check the lengths [i]AC[/i] and [i]BC[/i] .[br][/size][size=150]Make conclusions below.[/size]
[size=150]What can you conclude about [b][color=#9900ff]any point[/color][/b] that lies on the [color=#bf9000][b]perpendicular bisector[/b][/color] of a [b][color=#666666]segment[/color][/b]? [br][br][b]Hint: [/b] What did you notice about the [b][color=#9900ff]purple point [/color][/b]no matter where you put it? [/size]
[size=150]It is equidistant from the ends of the line segment that the perpendicular bisector is bisecting[/size]