# Thread: Help with a proof!

1. ## Help with a proof!

I've been trying to do this problem for a while but I am god awful at proofs and can't seem to make progress. Can someone please help me with a two column proof? The question is:

If triangle ABC is isosceles, with AB = AC, then the medians drawn from vertices B

and C must have the same length. Write a two-column proof of this result.

Any help is greatly appreciated.

Thanks!!!

2. ## Re: Help with a proof!

Originally Posted by tpask1998
I've been trying to do this problem for a while but I am god awful at proofs and can't seem to make progress. Can someone please help me with a two column proof? The question is:

If triangle ABC is isosceles, with AB = AC, then the medians drawn from vertices B

and C must have the same length. Write a two-column proof of this result.

Any help is greatly appreciated.

Thanks!!!
Ok suppose you've got isoceles triangle BAC where AB=AC

Draw the medians from B and C say BX and CY (X is the midpoint of AC, Y is the midpoint of AB)

Now, there are two triangles CYB and BXC

XC=YB because they are both 1/2 the length of two equal length segments AC and AB

Because BAC is isoceles B=C

BC=CB is common to both triangles.

So you have side-angle-side of two triangles, CYB and BXC, being equal and thus the two triangles are congruent.

Thus the lengths of BX and YC are equal.

You can take all this and convert it to a 2 column proof.