Formal Reasoning math help help help!!!?

Question

In the following diagram, ÐK = ÐN and KL = NM. Prove that ÐJLM = ÐJML (be sure to reason logically, using any theorems you know.)

picture: http://i135.photobucket.com/albums/q127/brianneee-/sgds.jpg

Answer 1

I dont know the theorems that would say this, but...

The line JM intersects the line KN, line JL also intersects line KN causing two segments KL and NM, because the two triangles have the same angles at K and N, KJ and NJ must be the same length, we then know that triangles KLJ and NMJ are congruent (Side Angle Side), and because JML and JMN are complementerary (add up to 90 degrees). The same thing about JLK and JLM, and since JMN = JLK, then their complements would be the same.

Answer 2

I assume the funky D with the line through it is the angle symbol?

Since angle K = angle N, triangle JKN is isosceles and KJ = NJ. Since KL = MN, then triangle KLJ is congruent to triangle MNJ (SAS), and JL = JM (corresponding parts).

Then triangle JLM is isosceles and so angle L = angle M.