Proof Problem #5

red green

Show that the area of the blue right-angled triangle is equal to the green area subtracted from the red area.

6 thoughts on “Proof Problem #5

  1. This took a while (15 mins), but appealing to the fact that for ANY similar shapes drawn on the sides of a right angled triangle the result comes out in one line. Nice!

  2. Love it. Not tried to solve it yet but looks good! Really cool style of problem for discussion with pupils, thanks.

  3. Nice use of Pythagorean theorem: the surface of the half disk with the hypotenuse as its diameter is the sum of the areas of the half disks having the two other sides as their diameters. The result easily follows.

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