SOLUTION: Prove: Quadrilateral ABCD is a parallelogram. Proof: Statement Reason 1. AC and BD bisect each other. given 2. AE = EC BE = ED definition of bisection 3. m∠AEB =

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Question 1085704: Prove: Quadrilateral ABCD is a parallelogram.
Proof:
Statement Reason
1. AC and BD bisect each other. given
2. AE = EC
BE = ED definition of bisection
3. m∠AEB = m∠CED
4. ΔABE ≅ ΔCDE SAS criterion
5. ∠ACD ≅ ∠CAB Corresponding angles of congruent triangles are congruent.
6. converse of Alternate Interior Angles Theorem
7. m∠BEC = m∠AED Vertical Angles Theorem
8. ΔBEC ΔDEA SAS criterion for congruence
9. DBC ≅ BDA Corresponding angles of congruent triangles are congruent.
10. converse of Alternate Interior Angles Theorem
11. Quadrilateral ABCD is a parallelogram. definition of a parallelogram
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
Prove: Quadrilateral ABCD is a parallelogram.
Proof:
Statement Reason 
1.  AC and BD bisect each other.	given
2. AE = EC                                      
   BE = ED	definition of bisection
3. m∠AEB = m∠CED	
4. ΔABE ≅ ΔCDE	SAS criterion
5. ∠ACD ≅ ∠CAB	Corresponding angles of congruent triangles are congruent.
6.	converse of Alternate Interior Angles Theorem
7. m∠BEC = m∠AED	Vertical Angles Theorem
8. ΔBEC ΔDEA	SAS criterion for congruence
9. DBC ≅ BDA	Corresponding angles of congruent triangles are congruent.
10.	converse of Alternate Interior Angles Theorem
11. Quadrilateral ABCD is a parallelogram.


Probably this proof is correct.

The deficiency of this post is the absence of what is given.

Therefore, the reader should scan the text again and again to connect all the ends.


See the lessons
    - In a parallelogram, each diagonal divides it in two congruent triangles
    - Properties of the sides of a parallelogram
    - Properties of the sides of parallelograms
    - Properties of diagonals of parallelograms
    - Opposite angles of a parallelogram
    - Consecutive angles of a parallelogram
in this site.


Also,  you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lessons are the part of this textbook under the topic "Properties of parallelograms".



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