Question 732347
1) Given
2)Angle BCA is congruent to Angle DCE: Vertical Angles are Congruent*
3)Triangle ABC is congruent to DEC: SAS (side-angle-side)**
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*Vertical angles are angles across from each other when two lines intersect. Vertical angles are always congruent. ACB and DEC are a pair of vertical angles, and BCD and ACE are a pair of vertical angles.
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**Side-Angle-Side (SAS) is a congruence shortcut for triangles. When two pairs of congruent sides an one pair of congruent angles (between the sides) are in two triangles, we can assume the triangles are congruent.  Scan through this PDF to learn more about congruence shortcuts: <a href="http://www.palisadessd.org/cms/lib03/PA01000106/Centricity/Domain/225/Ch_4_Triangle_Congruence_Shortcut_Investigation_Key.pdf">http://www.palisadessd.org/cms/lib03/PA01000106/Centricity/Domain/225/Ch_4_Triangle_Congruence_Shortcut_Investigation_Key.pdf</a>