How Can This Be True?
Although ABC and DEF both appear to be triangles, they are not. If you draw a straight line from A to B, the point M will be slightly below it. If you draw a straight line from D to E, the point P will be slightly above it.
If AB were a straight line, then ANM would have to be similar to MOB. That is, the slope of AM would have to be the same as the slope of MB. But the slope of AM is
and the slope of MB is
If ABC were a triangle, its area would be
Similarly if DEF were a triangle, its area would be
But if we add up the areas of the pieces of ABC we get a different result
red triangle = 12
green triangle = 5
L-shaped orange object = 7
L-shaped green object = 8
for a total area of 32 square units.
If we add up the areas of the pieces of DEF we get 33 square units, the same as for ABC plus one more for the white square.
So, ABC is slightly less than a triangle and DEF is slightly more than a triangle. Look closely.
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