Look at the figure below:

Triangle EFD has the measure of angle EFD equal to 60 degrees. G is a point on side DF. Points E and G are joined by a straight line. Angle DEG measures 60 degrees.

Make a two-column proof showing statements and reasons to prove that triangle DEF is similar to triangle DGE.

Question

Look at the figure below:

Triangle EFD has the measure of angle EFD equal to 60 degrees. G is a point on side DF. Points E and G are joined by a straight line. Angle DEG measures 60 degrees.

Make a two-column proof showing statements and reasons to prove that triangle DEF is similar to triangle DGE.

blanablas · Answer

One second, I'll get a better picture.

blanablas · Answer

Also, if anyone would like to give a detailed explanation of why their answer is true, it would be appreciated.

hedgepig · Answer

So let's think. How do we prove similarity?

blanablas · Answer

Through things like AAA, meaning all angles are the same, or SSS, as in all sides are the same.

hedgepig · Answer

is it AAA or AA?

blanablas · Answer

AA, typo.

hedgepig · Answer

Okay. So let's look at the picture. are we given similar sides or are we given congruent angles?

blanablas · Answer

Congruent angles

blanablas · Answer

I got that far before I got stuck on where to go next.

blanablas · Answer

I was thinking of whether side EG was an altitude, but that wasn't stated.

blanablas · Answer

Ok

blanablas · Answer

So with setting angle D as x

hedgepig · Answer

Made a mistake; let me look at this problem. One moment.

blanablas · Answer

Ah, ok.

hedgepig · Answer

Proceed with setting that angle as x. I read the problem wrong; tried to prove two of the wrong triangles are similar. Oops.

blanablas · Answer

Ok

blanablas · Answer

So with because angle D = D by the reflexive property

blanablas · Answer

And angle DEG = DFE by the definition of congruent angles

hedgepig · Answer

Yes.

blanablas · Answer

That means triangle DEF should be similar to triangle DFE by AA-similarity

hedgepig · Answer

Yup.

blanablas · Answer

Wait, said the wrong triangle

blanablas · Answer

meant triangle DEG ~ DFE

hedgepig · Answer

Apologies, I'm not checking the specifics here... good catch

blanablas · Answer

Thanks

hedgepig · Answer

Looks like you more or less got this one on your own, but feel free to continue post more questions if you find difficulties.

blanablas · Answer

Ok, thanks!

blanablas · Answer

One last question: What is the principle that states triangle DFE would be similar to triangle DEF?

hedgepig · Answer

You already stated it.
AA-similarity

blanablas · Answer

:P Oh yea

blanablas · Answer

I kept on thinking there was some special principle for it, thanks