Question 541598: 
I had a bit of time finding the right image to use. This is pretty much what I'm working with, only it's stands like an hourglass and the base and top extend out farther. (It should also say line AB, line DC and the midpoint on the bisected lines should say E. Also, if there's _?_ then (), then it's where I have to fill out. Everything else is what my textbook says.)
Given: Line segment AB is congruent to line segment DC
Line segment AD and line segment BC bisect each other.
Line AB || line CD
Prove: ▲ ABE is congruent to _?_ (▲ DCE)
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 angle bisector
4. line segment BE is congruent to line segment CE-------------4. _?_ (Def. of angle bisector)
5. line AB || line CD-----------------------------------------------5. _?_ (Given)
6. angle BAE is congruent to angle CDE------------------------6. _?_
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
(Feel free to correct my answers as well)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! If I understand you, your drawing looks sort of like this:
 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
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