How it works ?

In the applet below, the angle bisector of the ANGLE BAC is shown. Point E is a point that lies on this angle bisector. (Feel free to drag it around.)Before completing the directions below, move/drag points B, A, and/or C around to verify that the pink ray still remains an angle bisector of ANGLE BAC.Directions:1) Use the tools of GeoGebra to measure the distance from E to each side (ray) of ANGLE BAC.(Note: It should be obvious to you that this is not the same as finding EB and EC. Think about what you need to do.)2) What do you notice?3) Now move point E along this angle bisector. Does your observation in (2) still hold true?4) Now move/drag points B, A, and/or C around. Does your observation in (2) still hold true?5) Use your observations above to complete the following statement:If a ______________ lies on the ________________ of an _______________, then that ______________ is _____________________ from the __________ of that ___________.6) Now prove this statement true using the format of a 2column proof.