Prove: The medians of a triangle are concurrent.

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Given triangle ABC, show that medians AE, BF and CD are concurrent.

 

Since F is the midpoint of AC, AF = FC and

.

Similarly,

and

Thus,

By the converse of Ceva's theorem, medians AE, BF and CD are concurrent. The point where these medians intersect is known as the centroid.


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