In an isosceles triangle ABC (AB = BC), the intersection point M of the medians is 4 cm

| December 29, 2020 | education

In an isosceles triangle ABC (AB = BC), the intersection point M of the medians is 4 cm from the base. Find the distance from point M to point B.

1. CК and AN – medians of triangle ABC.
2. According to the problem statement, point M is 4 cm away from the AC side, that is, it belongs to the perpendicular drawn to the AC side.
3. Draw through this point the HВ height to the AC side.
4. By the condition of the problem, the triangle ABC is isosceles, therefore, the height of the ВН is also the median.
5. The point of intersection of the medians, according to their properties, divides each of them into two segments, related as 2: 1, starting from the top, that is, BM: НM = 2: 1.
ВM = 4 x 2 = 8 cm.
Answer: the distance from point M to point B is 8 cm.



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