are 6 triangles formed by 3 medians equal only in case of equilateral triangle? Because length of the sides and altitudes of triangles would be different in case of other triangles and hence area of ALC and BMC.

Nikhil, they are congruent in the case of an equilateral triangle. In a scalene triangle, only the area is same (as proved in the post). But they are not congruent. (In an isosceles triangle, we will have 3 pairs of congruent triangles – try proving it for yourself!)

thanks .. nice concept

Best of the best post I can have. ðŸ™‚ :thumbsup:

are 6 triangles formed by 3 medians equal only in case of equilateral triangle? Because length of the sides and altitudes of triangles would be different in case of other triangles and hence area of ALC and BMC.

Nikhil, they are

congruentin the case of an equilateral triangle. In a scalene triangle, only theareais same (as proved in the post). But they are not congruent. (In an isosceles triangle, we will have 3 pairs of congruent triangles – try proving it for yourself!)regards

J

Will the area of all the six triangles formed by joining the medians be equal in case of any triangle?

Yes, that is precisely what I have proved above…

regards

J

thank you sir

This would help us solve some of the seemingly very difficult problems in very less time

i tried proving it and i got them with equal area

please let me know if i am going wrong here