The corresponding angles of similar triangles are equal:



Angle PMK = Angle KLR    (1)

Angle PKM = Angle KRL    (2)

Angle KPM = Angle RKL    (3)



Now you can conclude from (3) that KL || PQ  (if the corresponding angles of two lines cut by a transversal are equal, then those two lines are parallel)



Angle 1 = angle PMK  (alternate interior angles of parallel lines cut by a transversal are equal)



Angle 2 = angle KLR  (corresponding angles of parallel lines cut by a transversal are equal)



Therefore angle 1 = angle 2   (by the above two statements and (1))



 

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