Day 1: Triangles and similarity
If the sum of the squares of the lengths of the two smaller sides of a triangle equals the square of the length of the third side, then the angle opposite the third side is a right angle. Because 32 + 42 = 52 (that is, 9 + 16 = 25), a triangle whose sides have the lengths 3, 4, and 5 will thus have a right angle opposite the side whose length is 5. ................
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