Prove that the medians to the equal sides of an isosceles triangle divide each other into respectively equal parts
The Attempt at a Solution
suppose we have a triangle ABC where AB = AC. Let D be the point on AB in which the median intersects AB, and let E be the point on AC in which the other median intersects AC. Consider triangles ACD and ABE. We know AC = AB. Also AD = AE because the medians are bisecting two congruent lines. Also note that ∠CAD = ∠BAE. Therefore triangle ACD is congruent to triangle ABE by SAS. It follows that the medians CD and BE are congruent.
This is as far as i get. I can show that the medians are congruent, but I do not know how to show they divide each other into equal line segments