Prove that the diagonals of a trapezoid, one of whose bases is twice as long as the other, divide its midsegment into three equal parts.

Asked May 01 '20 at 20:25

Active May 01 '20 at 20:25

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I am not sure where to start. A hint would be great to start off this problem.

asked May 01 '20 at 20:25

Mikal Jardin

1

A diagram is key. Start there. Then look for similar triangles. – quasi May 01 '20 at 20:41
Can you use the theorem that, in any triangle $ABC$, the line segment joining the midpoints of $AB$ and $AC$ is half as long as $BC$? If so, it can simplify your work here. If not, then I think you should try to prove that triangle theorem yourself (using similar triangles, as @quasi suggests). – Andreas Blass May 01 '20 at 21:54
Extend the legs of the trapezoid to form a triangle. – judith Khan May 08 '20 at 13:35

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