The figure below shows a trapezoid ABCD with
EF parallel to BC = a, and AD = b. If area AEFD = area EBCF, prove that
EF is the root mean square of a and b, that is,
.
Geometry problem solving is one of the
most challenging skills for students to learn. When a problem
requires auxiliary construction, the difficulty of the problem
increases drastically, perhaps because deciding which
construction to make is an illstructured problem. By
“construction,” we mean adding geometric figures (points, lines,
planes) to a problem figure that wasn’t mentioned as "given."
