<PRE><B>Question 1003919</B>
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If I knew that angle A and angle C were congruent. As well as angle B and angle D were congruent. How would I prove that ABCD is a {{{highlight(parallelogram)}}}.
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From the condition, &amp;nbsp;you have &amp;nbsp;&amp;nbsp;&lt;I&gt;L&lt;/I&gt;&lt;B&gt;A&lt;/B&gt; + &lt;I&gt;L&lt;/I&gt;&lt;B&gt;B&lt;/B&gt; = &lt;I&gt;L&lt;/I&gt;&lt;B&gt;C&lt;/B&gt; + &lt;I&gt;L&lt;/I&gt;&lt;B&gt;D&lt;/B&gt;.


In addition, &amp;nbsp;you know that the sum of internal angles of a quadrilateral is &amp;nbsp;360°.


It implies that &amp;nbsp;&amp;nbsp;&lt;I&gt;L&lt;/I&gt;&lt;B&gt;A&lt;/B&gt; + &lt;I&gt;L&lt;/I&gt;&lt;B&gt;B&lt;/B&gt; = &lt;I&gt;L&lt;/I&gt;&lt;B&gt;C&lt;/B&gt; + &lt;I&gt;L&lt;/I&gt;&lt;B&gt;D&lt;/B&gt; = 180°.


In other words, the sum of two consecutive angles in your quadrilateral is 180° for any two consecutive angles.


It implies that your quadrilateral is a parallelogram. 


(Because two consecutive angles are &amp;nbsp;&lt;U&gt;interior angles at the same side&lt;/U&gt;&amp;nbsp; of two lines transversed by the third line. 

Therefore, &amp;nbsp;these two lines are parallel. &amp;nbsp;See the lesson &amp;nbsp;&lt;A HREF=http://www.algebra.com/algebra/homework/Angles/Parallel-lines.lesson&gt;Parallel lines&lt;/A&gt;&amp;nbsp; in this site).


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