Construction of the Harmonic Mean in a Trapezoid

by Shannon Umberger

Given trapezoid KLMN, with KL // NM, KL = a, and NM = b.

Construct diagonals KM and LN. Construct their point of intersection and call it point R.

Construct a line parallel to base NM through point R. Construct the intersection of this line and leg KN and call it point P. Construct the intersection of the same line and leg LM and call it point Q.

Construct segment PQ. The length of this segment is the harmonic mean, "H," of the bases KL and NM.

Double check the construction by taking measurements and using the equation for finding the harmonic mean.

Return to Essay # 3 - Some "Mean" Trapezoids