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in laymans terms
just similar enough to look the same. Therefore the ratio between triangle A's other two sides is not the same as the ratio between triangle B's other two sides. You can count the squares - the larger triangle is 3 by 8, the other is 2 by 5, and 3/8 does not equal 2/5. The pay-off is that, when you use the two triangles to describe a rectangle as done in the diagram, the orientation of the two triangles matters as to the areas of the rectangles. Obviously 2 times 8 does not equal 3 times 5. Indeed, the difference is one, which is where the extra square comes from. If the hypotenuses actually *did* have the same gradient though, the orientation of the triangles wouldn't matter, as your intuition suggests.