Given a triangle ABC with a right angle B. Find the length of the median BM if AM = 8cm.

On the continuation of the median of the BM, we postpone the segment of the DM equal in length to the median of the BM. DM = ВM.

Let’s connect points A, D and C, D.

In the quadrangle ADCB, AM = CM by condition, BM = DM by construction.

Then the quadrilateral ADCB is a parallelogram in which the diagonals are halved.

Since the angle ABC = 90, then the parallelogram ADCB is a rectangle.

Then AC = BD, AM = BM = DM = CM = 8 cm.

Answer: The length of the median BM is 8 cm.