HELP PLEASE MEDAL AND FAN!

Question

bia_gonzalex · Answer

attachment

bia_gonzalex · Answer

@pyxieyt

bia_gonzalex · Answer

@Directrix

bia_gonzalex · Answer

attachment

pyxieyt · Answer

|dw:1448346347696:dw|What do you know about the diagram

bia_gonzalex · Answer

That C and E are intersecting A and D

bia_gonzalex · Answer

??

pyxieyt · Answer

Okay, so lets think about this! It is given that ABC is congruent to DEC and GFE is congruent to DEC too, right?

bia_gonzalex · Answer

i believe so

pyxieyt · Answer

Do you know the AA (Angle-Angle) Similarity?

bia_gonzalex · Answer

nope

pyxieyt · Answer

AA (Angle-Angle) Similarity: In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar.

bia_gonzalex · Answer

so the asnwer is Vertical angle thorem?

pyxieyt · Answer

It is proven by the AA (Angle-Angle) Similarity that ΔABC ~ ΔGEF

pyxieyt · Answer

Here is a link about it if you need more information http://hotmath.com/hotmath_help/topics/aa-similarity.html

pyxieyt · Answer

Here is link showing the angles http://prntscr.com/96a87e

bia_gonzalex · Answer

so is the answer It is proven by the AA (Angle-Angle) Similarity that ΔABC ~ ΔGEF?

pyxieyt · Answer

Yep! It would also be helpful to add the definition of the AA (Angle-Angle) Similarity (In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar.)

pyxieyt · Answer

This is the link showing you the corresponding angles http://prntscr.com/96a87e

pyxieyt · Answer

@bia_gonzalex

pyxieyt · Answer

Wait that is not the answer! I did not notice they switched the letters!!!

pyxieyt · Answer

ABC and DEC are congruent.
GFE and DCE are congruent too. 
 If you change the order of the letters DCE to DEC, then I must change the order of letters GFE to GEF.  Thus, GEF and DEC are congruent making ABC and GEF congruent!