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The two big triangles are not the same. The red triangle has a slope of 3/8 but the teal triangle has a slope of 2/5. This means the “hypotenuse” of the big triangle is not a straight line. It bulges in in the first big triangle then bulges out in the second big triangle to make room for the extra space.

In other words, the 1st large triangle is not a triangle at all. What appears to be the hypotenuse of a right triangle is, in fact, two sides of a quadrilateral. They just happen to meet at an angle of 181.2º – so close to 180º that it’s indistinguishable to the eye. I love it.

The two big triangles are not the same. The red triangle has a slope of 3/8 but the teal triangle has a slope of 2/5. This means the “hypotenuse” of the big triangle is not a straight line. It bulges in in the first big triangle then bulges out in the second big triangle to make room for the extra space.

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http://www.geogebratube.org/student/m10359

Go here for an interactive version of this triangle which makes it much easier to see what’s going on.

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In other words, the 1st large triangle is not a triangle at all. What appears to be the hypotenuse of a right triangle is, in fact, two sides of a quadrilateral. They just happen to meet at an angle of 181.2º – so close to 180º that it’s indistinguishable to the eye. I love it.

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Everyone already knew this.

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… EVERYONE!

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