The basic proportionality theorem says if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. You can prove it by linking the two smaller triangles it creates to the bigger one using their equal heights and bases—the area ratios lock the side ratios in place. Honestly, I think of it like setting up the warp threads on the loom: if your parallel lines are perfectly spaced, the proportions of the pattern always come out right.
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