[color=#000000]In the applet below, the [/color][color=#c27ba0][b]angle bisector[/b][/color][color=#000000] of the ANGLE [i]BAC [/i]is shown.  [br]Point [/color][color=#c27ba0][i]E [/i]is a point that lies on this angle bisector.  (Feel free to drag it around.)[br][br][/color][br][color=#000000]Before completing the directions below, [/color][color=#274e13]move/drag points [i]B[/i], [i]A, [/i]and/or [i]C[/i] around[/color][color=#000000] to verify that the[/color][color=#c27ba0] [b]pink ray[/b] [/color][color=#000000]still remains an [/color][color=#c27ba0][b]angle bisector[/b] [/color][color=#000000]of ANGLE [i]BAC[/i].  [/color][br][color=#000000] [/color][br][color=#ff0000][b]Directions: [/b][/color][br][color=#000000][br]1) Use the tools of GeoGebra to measure the distance from [i]E[/i] to each side (ray) of [br]    ANGLE [i]BAC.[br][/i]    (Note: It should be obvious to you that this is [b]not[/b] the same as finding [i]EB[/i] and [i]EC[/i].[br]     Think about what you need to do.)   [br] [/color][br][color=#000000]2) What do you notice?  [br][br]3) Now move [/color][color=#c27ba0]point [i]E[/i][/color][color=#000000] along this [/color][color=#c27ba0]angle bisector[/color].  [color=#000000]Does your observation in (2) still hold true?[br][/color][br][color=#000000]4) Now [/color][color=#274e13]move/drag points [i]B[/i], [i]A, [/i]and/or [i]C[/i] around.[/color] [color=#000000]Does your observation in (2) still hold true?[br][br][/color]    

[color=#000000]5) Use your observations above to complete the following statement:  [br][br]   [/color][color=#980000][b] If a ______________ lies on the ________________ of an _______________, then that[br][br]    ______________ is _____________________ from the __________ of that ___________.  [/b][/color][br][br][color=#000000]6) Now prove this statement true using the format of a 2-column proof.  [/color]