Question 1085704
.
Prove: Quadrilateral ABCD is a parallelogram.

Proof:
Statement	Reason

<pre>
1.  AC and BD bisect each other.	given
2. AE = EC                                      
   BE = ED	definition of bisection
3. m&#8736;AEB = m&#8736;CED	
4. &#916;ABE &#8773; &#916;CDE	SAS criterion
5. &#8736;ACD &#8773; &#8736;CAB	Corresponding angles of congruent triangles are congruent.
6.	converse of Alternate Interior Angles Theorem
7. m&#8736;BEC = m&#8736;AED	Vertical Angles Theorem
8. &#916;BEC &#916;DEA	SAS criterion for congruence
9. DBC &#8773; BDA	Corresponding angles of congruent triangles are congruent.
10.	converse of Alternate Interior Angles Theorem
11. Quadrilateral ABCD is a parallelogram.
</pre>


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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/In-a-parallelogram-each-diagonal-divides-it-in-two-congruent-triangles.lesson>In a parallelogram, each diagonal divides it in two congruent triangles</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Properties-of-the-sides-of-a-parallelogram.lesson>Properties of the sides of a parallelogram</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Properties-of-the-sides-of-parallelograms.lesson>Properties of the sides of parallelograms</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Properties-of-diagonals-of-parallelograms.lesson>Properties of diagonals of parallelograms</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Opposite-angles-of-a-parallelogram-are-congruent.lesson>Opposite angles of a parallelogram</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Consecutive-angles-of-a-parallelogram.lesson>Consecutive angles of a parallelogram</A>

in this site.



Also, &nbsp;you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> 

in this site.


The referred lessons are the part of this textbook under the topic "<U>Properties of parallelograms</U>".