PROBLEM: Isosceles Trapezoid

Click **here**
for a statement of the problem.

Discussion/Solution? : Isosceles Trapezoid

- The length, in terms of
**a** and **b**, of a parallel line
segment through the midpoints of the slant sides of the isosceles trapezoid
is

.
This is the arithmetic mean. The segment is also known as the median
of the trapezoid.

Click **here** for GSP script.

- The length, in terms of
**a** and **b**, of a parallel line
segment through the intersection of the diagonals of the isosceles trapezoid
is

.
This is the harmonic mean.

Click **here** for GSP script.

- The length, in terms of a and b, of a parallel line segment that divides
the isosceles trapezoid into two isosceles trapezoids of equal area is

.
This is the geometric mean.

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- The length, in terms of
**a** and **b**, of a parallel line
segment that divides the isosceles trapezoid into two isosceles trapezoids
of equal area is

.
This is the root mean squared.

Click **here** for GSP script.

**Comparing the lengths of the four segments**

Click **here** for a GSP sketch to examine
the segments.

Consider the proofs of the inequalities.

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