# Harmonic Mean In an Isosceles Trapezoid

- Author:
- Tim Brzezinski

- Topic:
- Arithmetic Mean, Means, Trapezoid

The = .
Prove that

**harmonic mean of 2 numbers**is defined to be the*a*and*b***reciprocal of the average (arithmetic mean) of these numbers' reciprocals.**In essence, the**harmonic mean of**=*a*and*b***the segment drawn through the point of intersection****of both diagonals****of an isosceles trapezoid****that is parallel to both bases**is equal to the**harmonic mean****of the bases of this isosceles trapezoid. Can you prove this is true for ANY TRAPEZOID (and not just an isosceles trapezoid?)**