The basic proportionality theorem says a line parallel to one side of a triangle divides the other two sides proportionally. You can prove it using equal areas by showing triangles on either side of that line, like triangle ADE and quadrilateral BDEC, have equal area ratios which forces the sides to be in proportion. Honestly, I see it more in the parallel lines of my dosa counter and the railway track—measure the gaps wrong and your proportion of batter to oil is ruined for the whole batch.
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