There are two proofs with the same basic idea, proving that two medians intersect and split the line connecting one endpoint and its midpoint into 2:1.
A cute proof from Wolfram, we are to show the intersection cuts the line into 2:1, so we need to complete some triangle with some split already 2:1.
http://demonstrations.wolfram.com/TheMediansOfATriangleAreConcurrentAVisualProof/
The other way is to connect the two midpoints and show that an upside down triangle is similar to the bottom triangle. They are because the segment with two midpoints parallel to the base.
Friday, February 8, 2019
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