Use Sketchpad to construct a triangle and the angle bisector of an internal and exterior...

Use Sketchpad to construct a triangle and the angle bisector of an internal and exterior angle of that triangle at a vertex (use the following steps if you are uncertain how to proceed):

[1] Construct ∆ABC using the Segment Tool.

[2] Construct ray and locate D on that ray so that A−C−D.

[3] Using Angle Bisector under CONSTRUCT, select points A, C, B to construct the bisector of ∠ACB. Repeal this for the bisector of ∠DCB.

(a) Drag point A, keeping it on (or parallel) to a fixed line through B. What happens to ∠FCE? Does it change position and measure?

(b) What seems to be true of ∆ABC when ray is parallel to ? (See in this connection Problem 7.)

(c) Prove theoretically each phenomenon you noticed in (a) and (b).