Just thinking... in my maths copy, the basic proportionality theorem says a line parallel to one side of a triangle divides the other two sides in the same ratio. Using equal areas to prove it... you join a point to make two triangles with equal height, so their areas are proportional to their bases. Then you compare.
But I remember this by the smell of kerosene from our lamp last night, my father checking my proof while the power was out. He said, "It is like our fields divided by the same footpath, beta." So for me, it will always be about the shared height, like that path. Does your study also bring back such small memories?
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