Question 541598
If I understand you, your drawing looks sort of like this:
{{{drawing(250, 150, -10,10, -6,6,
triangle(-8,-5,3,-5,0,0),
triangle(8,5,-3,5,0,0),
locate (8,5,B), locate (-3.5,5,A),
locate (-8,-5,C), locate (3,-5,D), locate (0.5,0.5,E)
)}}} I agreed with most of your reasons, changed angle bisector to segment bisector (we are not bisecting any angles here, just the segments on the two transversals).
Statements----------------------------------------------------------- Reason
1. line segment AB is congruent to line segment DC--------------1. Given
2. line segment AD and line segment BC bisect each other------2. _?_ (Given)
3. line segment AE is congruent to line segment _?_ (DE)------3. Def. of segment bisector
4. line segment BE is congruent to line segment CE-------------4. _?_ (Def. of segment bisector)
5. line AB || line CD-----------------------------------------------5. _?_ (Given)
6. angle BAE is congruent to angle CDE------------------------6. _?_ If 2 || lines are intersected by a transversal, then the alternate interior angles are congruent
7. angle _?_ (ABE) is congruent to angle DCE-----------------7. If 2 || lines are intersected by a transversal, then the alternate interior angles are congruent
8. angle _?_ (AEB) is congruent to angle _?_ (CED)----------8. Vertical angles are congruent
9. ▲ ABE is congruent to ▲ DCE-------------------------------9. Definition of congruent polygons