Question 688884: Im doing proofs can you help me with this: Prove: In an equilateral triangle the three medians are equal.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Label your equilateral triangle vertices as A, B, and C. Label the intersection of the median from vertex A as D, from vertex B as E, and from vertex C as F.
Since a median connects a vertex with the midpoint of the opposite side, AF = FB, BD = DC, and CE = EA. But since ABC is an equilateral triangle, AB, BC, and CA are all congruent, therefore AF = FB = BD = DC = CE = EA. Then, since ABC is equilateral, it is also by definition equiangular.
Therefore, triangle ABD is congruent to triangle CBF which is in turn congruent to triangle CAF, all by SAS.
Then by CPCT, AD congruent to BE congruent to CF. QED.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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