Use Sketchpad, investigate the following phenomenon in connection with the remarks made c...

Use Sketchpad, investigate the following phenomenon in connection with the remarks made concerning Example 3.

[1] Construct ∆ABC using the Segment Tool.

[2] Locate point D on side , and E on side .

[3] Construct the midpoint F of .

[4] Construct so that F is its midpoint. (Mark the vector D to F, then translate F by Marked Vector, producing point F'. Then join D and F'.)

[5] Join points E and F', and display the distances DF and BC. (For extra effect, shade in the triangles ∆ADF and ∆FEF' using Polygon Interior under CONSTRUCT.)

Drag points D and E and write down your observations (there should be several). (Be sure to move E on top of point C in your experiment.) Did you rediscover the Midpoint Connector Theorem?