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PROBLEM: Isosceles Trapezoid

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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.

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• 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.

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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 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.

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Comparing the lengths of the four segments

Click here for a GSP sketch to examine the segments.


Consider the proofs of the inequalities.