Here is the question: suppose ABC is a right triangle with the right angle at C. Let M be the midpoint of the segment AB. Prove that the area of triangle AMC is the same as the area of the triangle MCB.

We know that MC=AM=CM. obviously MCB and AMC are isosceles triangles. But this is where I am stuck. I can't really prove that angle A or B are equal, nor the heights of the two triangles the same. Do I use some form of similar triangles? I think that is the process but I don't see how using similar triangles leads me to a congruency. Thank you for the help!!