The
Sum Of The Squares Of The Sides Of The Trapezoid
And The Pythagorean Theorem
Problem
The
Sum Of The Squares Of The Sides Of The Trapezoid
And The Pythagorean Theorem
Problem
Given: In the figure above on the left the triangle is a right triangle with a
line drawn connecting the midpoints of its shorter legs.
The smaller white triangle created is then to be removed leaving the blue trapezoid.
The blue trapezoid has sides a, b, c, and d.
This blue trapezoid is the same trapezoid shown in the figure on the right,
and squares are constructed on each of its sides as shown.
Show: algebraically that the sum of the areas of the three smaller red squares
is equal to one-half the area of the yellow square on the largest side of the trapezoid.
That is, show:
If this is true, then the sum of the areas of the six red squares shown in the figure below must be
equal to the area of the square on the diagonal of the blue hexagon shown there. Why?
2(a2 + b2 + c2) = d2
But this figure is strikingly similar to the next figure below,
