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&#8736;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!
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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.

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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".

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&#8736;AEB =

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 =