# Medians of an Isosceles triangle

1. Jan 28, 2014

### DotKite

1. The problem statement, all variables and given/known data

Prove that the medians to the equal sides of an isosceles triangle divide each other into respectively equal parts

2. Relevant equations

3. 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

2. Jan 28, 2014

### LCKurtz

Draw DE. You should be able to show triangle BDE is congruent to triangle CDE and that DE is parallel to BC. If O is where the medians intersect, show triangle DEO is similar to triangle BCO. That should give you the proportional sides you seek.