Prove that in a right-angled triangle, the median drawn from the vertex of the right angle is half the hypotenuse.

For proof, we will extend the median BM further, BM = MD. We will obtain a parallelogram of ABСD, since AM = MC (median), BM = MD (by construction). In a rectangle, the diagonals are equal, AC = BD, AM = MC, halved.

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