# 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**