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Prove that in an isoceles triangle two of the medians (the lines drawn from the vertex to the midpoint of the opposite side) are congruent.

FreezingTNT  Sep 11, 2018
edited by FreezingTNT  Sep 11, 2018
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Let ABC be an isosceles triangle  with  AB  = AC

 

Draw median BM to side  AC  and  median CN to side AB

 

Note that  since AB  = AC...then then the medians divide  AB and AC into two equal parts.....so....MC   = NB

And since  AB  = AC, then angle ABC  = angle ACB

And BC  = BC

 

So...by side-angle side.....triangle  MCB is congruent to triangle NBC

 

So...therefore....BM  = CN 

 

See this image : 

 

 

cool cool cool

CPhill  Oct 2, 2018

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