Question 221424
<s>I'm having a hard time visualizing the problem. Can you post an image of it? If you need help posting images, check out this <a href=http://www.algebra.com/algebra/homework/playground/lessons/posting-images.lesson>lesson</a>.</s>



The basic goal is to show that triangle ABC is congruent to triangle CED. From there, you can show that AC is congruent to EC because their corresponding parts are congruent.



Here's another way to prove this in a two column proof:


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/table2.png">


Notes:


1) CPCTC stands for <a href=http://en.wikipedia.org/wiki/CPCTC><i><b>C</b>orresponding <b>P</b>arts of <b>C</b>ongruent <b>T</b>riangles are <b>C</b>ongruent</i></a>.


2) I used the theorems and postulates from <a href="http://regentsprep.org/Regents/mathb/1b/theorems.htm">this page</a> and <a href="http://quizlet.com/595128/ccds-geometry-theorems-postulates-and-properties-flash-cards/">this page</a>


3) In statement 5, recall that vertical angles are congruent to one another.


4) AAS stands for <a href=http://en.wikipedia.org/wiki/Congruence_%28geometry%29#Determining_congruence>Angle Angle Side</a>. I used the angles ACB and DCE for the first 'A', the angles ABC and CDE for the second 'A', the sides AB and DE for the 'S'