Math CentralQuandaries & Queries


Question from Nazrul, a teacher:

If two medians of a triangle are equal , how can I prove that the triangle is isosceles.


First draw an accurate figure: Label the triangle ABC with E the midpoint of AC and F the midpoint of AB. You are given that the medians AE and BF are equal, so you should draw your figure with AE = BF. AE intersects BF at the center of gravity G, so what do you know about the ratios BG:GE and CG:GF? This knowledge immediately gives you similar isosceles triangles BGC and EGF. From here you can easily prove that BF = CE (or, if you prefer, that the angles CBA = BCA).


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