Prove that in an isoceles triangle two of the medians (the lines drawn from the vertex to the midpoint of the opposite side) are congruent.

FreezingTNT
Sep 11, 2018

#1**+1 **

Let ABC be an isosceles triangle with AB = AC

Draw median BM to side AC and median CN to side AB

Note that since AB = AC...then then the medians divide AB and AC into two equal parts.....so....MC = NB

And since AB = AC, then angle ABC = angle ACB

And BC = BC

So...by side-angle side.....triangle MCB is congruent to triangle NBC

So...therefore....BM = CN

See this image :

CPhill
Oct 2, 2018