SOLUTION: AC =~ DC and BC =~ CE. Prove Triangle ABC =~ to Triangle DEC. <a href="http://imgur.com/nAx7TZa"><img src="http://i.imgur.com/nAx7TZa.png" alt="" title="Hosted by imgur.com" /></a

Algebra ->  Geometry-proofs -> SOLUTION: AC =~ DC and BC =~ CE. Prove Triangle ABC =~ to Triangle DEC. <a href="http://imgur.com/nAx7TZa"><img src="http://i.imgur.com/nAx7TZa.png" alt="" title="Hosted by imgur.com" /></a      Log On


   

Question 732347: AC =~ DC and BC =~ CE. Prove Triangle ABC =~ to Triangle DEC.
Found 2 solutions by lynnlo, ohtheirony:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ohtheirony(35) About Me  (Show Source):
You can put this solution on YOUR website!
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)**


*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.


**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: http://www.palisadessd.org/cms/lib03/PA01000106/Centricity/Domain/225/Ch_4_Triangle_Congruence_Shortcut_Investigation_Key.pdf