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

Question 732347: AC =~ DC and BC =~ CE. Prove Triangle ABC =~ to Triangle DEC.

Found 2 solutions by lynnlo, ohtheirony:
Answer by lynnlo(4176) (Show Source): You can put this solution on YOUR website!

Answer by ohtheirony(35) (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
RELATED QUESTIONS
Triangle ABC is isosceles, with Line AB=AC, and Line BC=39 cm A square is inscribed in... (answered by MathLover1)
Triangle ABC below is isosceles, with AB=AC. A square is inscribed in the triangle, with... (answered by ikleyn)
ok, so i have a sideways hourglass looking figure 2 triangles obviously. starting at the... (answered by Edwin McCravy)
In the diagram below, Line BD=6 cm and Line DC=2 cm. Find the ratio of the area of the... (answered by math_helper)
imgur.com/a/6nVwylD (answered by ikleyn)
Perform the indicated operation and expression lowest terms. Thanks for any help. (answered by CubeyThePenguin)
Perform the indicated operation and expression lowest terms. (answered by CubeyThePenguin)
https://imgur.com/mlmAPzV In the diagram, angles marked are equal. BD = 4 cm and BC = 10... (answered by ikleyn)
(answered by fractalier)