The height BH and the median CM are plotted in triangle ABC. Find the length of the segment HM if AM = 3, AH = HC.

univerkov | February 26, 2021 | education

Since, according to the condition, AH = CH, then the height of the ВН divides the side of the AC in half, and then the height of the ВН is also the median, which means that the triangle ABC is isosceles with the base of the AC.

CM is the median of the triangle, then AB = 2 * AM = 6 cm, and then BC = 6 cm

Points M and H are the middle of the sides AB and AC, then the segment CM is the middle line of the triangle ABC, and then HM = BC / 2 = 6/2 = 3 cm.

Answer: The length of the НM segment is 3 cm.

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