Question

Geometry help!!

Answer 1

You answer will be C, Angle Side Angle (ASA).  Since you are given two lines parallel, then you know angle BCE and angle CEF are congruent using the reason of "If two lines are parallel then the alternate interior angles are congruent" (they are congruent because they are alternate interior angles). Also, angle CBF and angle BFE are congruent because they are both alternate interior angles.  
 
P.S. the first pair of alternate interior angles is created by parallel lines BC and EF and the intersecting line BF.  And the second pair is created by parallel lines BC and EF and intersecting line CE.