In the figure below, ∠ABC ≅ ∠DEC and ∠GFE ≅ ∠DCE. Point C is the point of intersection between segment AG and segment BD while point E is the point of intersection between segment AG and segment DF.

Question

anonymous · Answer

Prove ΔABC ~ ΔGEF.

anonymous · Answer

@dmezzullo

nikato · Answer

|dw:1389320289is goven889:dw|ok, so this is what is given

nikato · Answer

|dw:1389320396539:dw|what else can u say about the diagram?

anonymous · Answer

That C and E are intersecting A and D

anonymous · Answer

@nikato

anonymous · Answer

@ranga

nikato · Answer

what do u know about vertical angles?

anonymous · Answer

I dont remember.

nikato · Answer

u would use that 2 times. and then using AA similarity, u can prove the 2 trianlges are similar

nikato · Answer

u should know a thoerem that states if 2 angles are vertical, then they are congrunet

anonymous · Answer

can you tell me with this symbol means "~"? I forgot what that means.

nikato · Answer

it means similar

anonymous · Answer

ok thanks.

ranga · Answer

It would be simpler to prove they are congruent and hence they are similar too.
ABC and DEC are congruent.  ----(1)
GFE and DCE are congruent too.  If I 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.  Compare it to (1) and we can see ABC and GEF are congruent and therefore similar too.

anonymous · Answer

http://assets.openstudy.com/updates/attachments/5224b58ee4b06211a67f8a64-akashdeepdeb-1378141049945-gfff.jpg

anonymous · Answer

@ranga can you look at the link

anonymous · Answer

@nikato