[color=#000000]In the applet below, note that[/color] [b][color=#ff0000]point [i]E[/i][/color] [color=#000000]is [/color][color=#9900ff]equidistant[/color][/b][color=#000000][b] from the SIDES of ANGLE [/b][i][b]BAC.[/b]  [/i]  [br][br][/color][b]Directions:[br][/b][color=#000000][br]1) Move the [/color][color=#9900ff]purple slider[/color][color=#000000] to adjust [/color][color=#ff0000]point [i]E [/i]'s [/color][color=#9900ff]distance from the[/color][color=#000000] sides of ANGLE [i]BAC. [br][/i]    As you do, you'll notice that all possible locations of point [i]E[/i] will be traced out.  [br][br]2) What does the[/color][color=#ff0000] locus (set) of points in the plane [/color][color=#9900ff]equidistant from the[/color][color=#000000] sides of an angle[br]    look like?   [i]Be specific!  [/i][br][br]3) Now move points [i]A[/i] and [i]B[/i] around to change the initial measure of the displayed angle.[br]    After doing so, hit the "clear trace" button to clear the previous traces of [i]E[/i].  [br][br]4) Repeat step (1).  Does your response for (2) above still seem valid?  [br][br]3) Use the tools of GeoGebra to show that your response in (2) above is true.  [br][/color]

[color=#000000]Use your observations from interacting with the applet above [br]to complete the following statement:  [/color][br][br][color=#ff0000][b]If a point is ____________________ from the ____________ of an ______________, then [br][br]that   __________________ lies on the ___________________ of that ________________.  [/b][/color][br][br][color=#000000]Now prove this theorem true using a 2-column format.  [/color][br]

[color=#000000]Interact with the applet below for a few minutes. Then, answer the questions that follow. Be sure to change the locations of the [/color][color=#1e84cc][b]BLUE POINT[/b][/color][color=#000000] and WHITE POINT(S) each time before you re-slide the slider. Be sure to adjust the [/color][b][color=#ff00ff]pink slider[/color][/b][color=#000000] as well! [/color]

[color=#000000][b]Questions: [br][br][/b][/color][color=#000000]1) What can you conclude about the [/color][color=#980000][b]distances[/b][/color][color=#000000] from the [/color][color=#1e84cc][b]blue point[/b][/color][color=#000000] to each [b]side[/b] of the angle?[br] How do you know this? [br][br]2) What can you conclude about the location of the [/color][color=#1e84cc][b]blue point[/b][/color][color=#000000] with respect to the original (larger) angle? [br] Explain how you know this. [br][br]3) Use your observation to fill in the blanks to make a true statement: [br] If a [/color][color=#1e84cc][b]point[/b][/color][color=#000000] is[/color][color=#980000][b] _____________________ [/b][/color][color=#000000]from the [b]sides[/b] of an angle, then [/color][color=#1e84cc][b]that point[/b][/color][color=#000000] lies on the [br][/color][color=#1e84cc][b] _______________[/b][/color][color=#000000] of that angle. [br][br] 4) Write a 2-column or paragraph proof that proves the statement in (4) true. [br] [/color]