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Question 761114: PLEASE HELP!I really don't understand how to do this.
Complete the following proof.
Prove: In an equilateral triangle the three medians are equal.
https://media.glynlyon.com/g_geo_2012/9/q415a.gif
This is how the answer looks:
http://assets.openstudy.com/updates/attachments/51ca4d0de4b063c0de5a6daf-leslie096-1372212537835-capture.png
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Our equilateral triangle lives in the Cartesian coordinate system. In this system, the distance between any two points is d = sqrt(( y2 - y1)^2 + (x2 - x1)^2 )
so lets calculate the length of each median
QA = sqrt ( (b/2 - 0)^2 + (3a/2 - 0)^2 ) = sqrt( b^2/4 + 9a^2/4 ) = sqrt((9a^2+b^2)/4)=(1/2)sqrt(9a^2+b^2)
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RB = sqrt ( (0 - b/2)^2 + (2a - a/2)^2 )
RB = sqrt ( b^2/4 + (4a/2 - a/2)^2 )
RB = sqrt ( b^2/4 + 9a^2/4)
RB = (1/2)*sqrt(9a^2+b^2)
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PC = sqrt ( (b-0)^2 + (a - a)^2 ) = sqrt (b^2) = b
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now each side is 2a so the altitude b is equal to
b = sqrt ( (2a)^2 - a^2 ) = sqrt (3a^2) = a*sqrt(3)
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note that PC is a median and it is equal to b = a*sqrt(3)
which means that QA and RB are also equal to a*sqrt(3)
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