SOLUTION: I have started this work and find myself stuck with the next steps. I would appreciate any tutor assistance to get me on track with the next few steps. The scenario is as follow

Question 886221: I have started this work and find myself stuck with the next steps. I would appreciate any tutor assistance to get me on track with the next few steps.
The scenario is as follows:
GIVEN:
Triangle LMN is isoceles with base LN
angle LMO is congruent to angle NMO
PROVE:
O is the midpoint of LN
Basically what I have as of now is this:
ML=MN
MLO=MNO
triangles congruent by SAS
Any assistance would be appreciated.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Note that MO bisects angle LMN and is perpendicular to LN
by Pythagorean theorem we have
LO^2 +MO^2 = LM^2 = MN^2 = MO^2 + ON^2
therefore
LO^2 = ON^2 and
LO = ON

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