document.write( "Question 688884: Im doing proofs can you help me with this: Prove: In an equilateral triangle the three medians are equal. \n" ); document.write( "

Algebra.Com's Answer #425714 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "Therefore, triangle ABD is congruent to triangle CBF which is in turn congruent to triangle CAF, all by SAS.\r
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\n" ); document.write( "\n" ); document.write( "Then by CPCT, AD congruent to BE congruent to CF. QED.\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "Egw to Beta kai to Sigma
\n" ); document.write( "My calculator said it, I believe it, that settles it
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