Prove that the medians of a triangle intersect at one point, which divides each median in a 2: 1 ratio, counting from the vertex.

In triangle ACB, draw medians AA1, BB1, CC1
Connect points B1 and A1
В1А1- the middle line of the triangle
Consider triangles AOB and A10B1:
Angle A1AB = angle B1A1A
Angle B1BA = angle BB1A1-as cross lying angles
Hence, the triangle AOB is similar to A1OB1
It follows from this that AO / A1O = BO / B1O = AB / A1B1
AB = 2A1B, which means AO = 2A1O, BO = 2B1O, CO = 2C1O