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Given: the medians divide a triangle into 6 smaller triangles. Prove: The area of all the...

Given: the medians divide a triangle into 6 smaller triangles.

Prove: The area of all the triangles are the same

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Answer #1

Median of a triangle divides the triangle into two triangles with equal area.

For consider and median . We got two triangles here and . Now both the triangles have bases namely and respectively and they're of equal length. Also height of both the triangles is equal. .

Now, are medians of triangles respectively.

So

Also has medians .

Hence, the area of all the 6 triangles is the same.

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