document.write( "Question 1085704: Prove: Quadrilateral ABCD is a parallelogram.\r
\n" ); document.write( "\n" ); document.write( "Proof:
\n" ); document.write( "Statement Reason
\n" ); document.write( "1. AC and BD bisect each other. given
\n" ); document.write( "2. AE = EC
\n" ); document.write( " BE = ED definition of bisection
\n" ); document.write( "3. m∠AEB = m∠CED
\n" ); document.write( "4. ΔABE ≅ ΔCDE SAS criterion
\n" ); document.write( "5. ∠ACD ≅ ∠CAB Corresponding angles of congruent triangles are congruent.
\n" ); document.write( "6. converse of Alternate Interior Angles Theorem
\n" ); document.write( "7. m∠BEC = m∠AED Vertical Angles Theorem
\n" ); document.write( "8. ΔBEC ΔDEA SAS criterion for congruence
\n" ); document.write( "9. DBC ≅ BDA Corresponding angles of congruent triangles are congruent.
\n" ); document.write( "10. converse of Alternate Interior Angles Theorem
\n" ); document.write( "11. Quadrilateral ABCD is a parallelogram. definition of a parallelogram \n" ); document.write( "
Algebra.Com's Answer #699969 by ikleyn(52787)\"\" \"About 
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\n" ); document.write( "Prove: Quadrilateral ABCD is a parallelogram.\r
\n" ); document.write( "\n" ); document.write( "Proof:
\n" ); document.write( "Statement Reason\r
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "1.  AC and BD bisect each other.	given\r\n" );
document.write( "2. AE = EC                                      \r\n" );
document.write( "   BE = ED	definition of bisection\r\n" );
document.write( "3. m∠AEB = m∠CED	\r\n" );
document.write( "4. ΔABE ≅ ΔCDE	SAS criterion\r\n" );
document.write( "5. ∠ACD ≅ ∠CAB	Corresponding angles of congruent triangles are congruent.\r\n" );
document.write( "6.	converse of Alternate Interior Angles Theorem\r\n" );
document.write( "7. m∠BEC = m∠AED	Vertical Angles Theorem\r\n" );
document.write( "8. ΔBEC ΔDEA	SAS criterion for congruence\r\n" );
document.write( "9. DBC ≅ BDA	Corresponding angles of congruent triangles are congruent.\r\n" );
document.write( "10.	converse of Alternate Interior Angles Theorem\r\n" );
document.write( "11. Quadrilateral ABCD is a parallelogram.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Probably this proof is correct.\r
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\n" ); document.write( "\n" ); document.write( "The deficiency of this post is the absence of what is given.\r
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\n" ); document.write( "\n" ); document.write( "Therefore, the reader should scan the text again and again to connect all the ends.\r
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\n" ); document.write( "\n" ); document.write( "See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - In a parallelogram, each diagonal divides it in two congruent triangles\r
\n" ); document.write( "\n" ); document.write( "    - Properties of the sides of a parallelogram \r
\n" ); document.write( "\n" ); document.write( "    - Properties of the sides of parallelograms \r
\n" ); document.write( "\n" ); document.write( "    - Properties of diagonals of parallelograms \r
\n" ); document.write( "\n" ); document.write( "    - Opposite angles of a parallelogram\r
\n" ); document.write( "\n" ); document.write( "    - Consecutive angles of a parallelogram\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook on Geometry\r
\n" ); document.write( "\n" ); document.write( "    GEOMETRY - YOUR ONLINE TEXTBOOK \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Properties of parallelograms\".\r
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