http://prntscr.com/7tdjo3

- anonymous

http://prntscr.com/7tdjo3

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- anonymous

@phi

- anonymous

@ParthKohli

- misssunshinexxoxo

Don't you see that abc and gfe are congruent?

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## More answers

- anonymous

Yes i do.

- anonymous

But with which property do i prove that with?

- misssunshinexxoxo

You should write out a proof for this.

- anonymous

Okay, but im not really good at this, could you walk me through it?

- misssunshinexxoxo

Sure review this https://www.wyzant.com/resources/lessons/math/geometry/triangles/angles_of_triangles

- phi

Here is what the first sentence tells us
< ABC =

##### 1 Attachment

- phi

write that statement and next to it write the reason we know it is true.
Do you know the reason?

- anonymous

No, i dont.

- phi

We are told it is true. the short reason is " given "

- anonymous

Oh okay.

- phi

so the first line of your proof should read
Statement Reason
< ABC =

- anonymous

Okay.

- phi

- anonymous

That angle GEF is similar to triangle DEC?

- phi

angles can only be "congruent" (or not!) to other angles.
but you should have learned about this fact:
|dw:1437055059934:dw|

- phi

if you have an "x", the angles opposite each other are congruent (equal to each other)
Notice that is also true
|dw:1437055171801:dw|

- anonymous

Ohhh...okay

- phi

Look at your problem. what angle is a vertical angle
to angle CED ?

- anonymous

angle GEF?

- phi

Yes. and angle GEF is part of the triangle we need to show is similar.
so we found a useful fact
write down the next line in the proof
Statement Reason
< ABC =

- anonymous

Yay! awesome...

- phi

I messed up the name of the angle. Better fix it
Statement Reason
< ABC =

- anonymous

lol, okay.

- phi

if

- anonymous

Well, i think that angle ABC and Angle GEF are congruent.. But not sure by which property it is proven.

- phi

"things equal to the same thing are equal to each other"
I think they also use the name "transitivity" (which is a fancy word for the first statement)

- anonymous

Okay.. So i would put that as:

- phi

so now the proof is
Statement Reason
< ABC =

- phi

yes

- anonymous

That would be it, right?

- phi

now we can add the other given statement

- anonymous

Oh okay

- phi

can you add that next line?
Here is the picture (I tried to add a blue line showing the two angles )

##### 1 Attachment

- anonymous

mmm...Im guessing here so i might be wrong...
Angles ABC and Angle GFE have corresponding angles? im not sure

- phi

Read the original problem. Do you see they tell us a second fact about 2 other angles?
add that info to your proof and write the reason

- anonymous

"Angle GEF is congruent to Angle DEC?"

- phi

Is that what they say? read it carefully

- anonymous

GFE*

- phi

They write:
In the figure below, ....
yes it is

- anonymous

DCE**

- phi

yes, it is painful keeping the letters in the right order... but it matters.
so what is the next statement we can add to the proof (and the reason)?

- anonymous

Angle GFE ≅ ∠DCE..... Idk by which reason.

- anonymous

By which reason??

- phi

yes, that is good. the reason is because we were told.

- anonymous

OH "given"

- anonymous

Thank you so much Phi! I appreciate it so very much <3

- phi

yes, given. Now notice that angle DEC is not part of the triangle we want.
but we can use the same reasoning that we did before.
so far we have
Statement Reason
< ABC =

- anonymous

um no

- phi

< DCE = what other angle ?

- anonymous

FGE?

- phi

what angle is a vertical angle of

- anonymous

EFG?

- anonymous

NOOO ABC

- phi

|dw:1437057224248:dw|

- phi

when you write down an angle, the "middle" letter is at the vertex
so you would write

- anonymous

okay..

- phi

can you write the next statement in the proof?

- anonymous

Angle DCE = ACB by vertical angles?

- phi

yes

- anonymous

awesome

- phi

Statement Reason
< ABC =

- phi

the reason is transitivity
next,
if two angles of a triangle are congruent, then the third angles are also
once you have all 3 angles congruent, you have proven the two triangles are similar

- anonymous

Thank you so so much! Sorry for leaving, my computer has been crashing a lot lately.

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