What If - Iteration #1
WHAT I DID ...
Constructed right triangle ABC.
Found midpt (D) of side AC. Placed a random point (E) on the hypotenuse AB.
Constructed a "pseudo-midline" (DE).
Measured AE, EB, BC, CD, DA, and DE.
Dragged E until DE = CD = DA.
WHAT I NOTICED ...
Looked like E was at the foot of the triangle (from point C).
So, I constructed CE and measured angle BEC.
Then, re-worked ideas (see What If - Iteration #2).