Question 178987
this proof is based on this drawing. In the future , since we dont have access to the problems people provide, try to describe it as best you can, so that we dont have to guess as to the form of the drawings.  Thanks Mathtut
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<img src="http://i11.photobucket.com/albums/a176/jabberstox/Untitled_img.gif">
  
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**************************************************************************
             statement                             reason
**************************************************************************
1.@B congruent @D                              1. Given
  BC congruent DC

2.ED // AB                                     2.converse alternate int.angles

3.@E congruent @B                              3.alt interior angles

4.tri ABC congruent tri ECD                    4.AAS

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AAS-if two angles and the non included side of one triangle are congruent to the corresponding parts of another triangle, the two triangles are congruent.