Don't you see that abc and gfe are congruent?
Yes i do.
But with which property do i prove that with?
You should write out a proof for this.
Okay, but im not really good at this, could you walk me through it?
Sure review this https://www.wyzant.com/resources/lessons/math/geometry/triangles/angles_of_triangles
write that statement and next to it write the reason we know it is true. Do you know the reason?
No, i dont.
We are told it is true. the short reason is " given "
so the first line of your proof should read Statement Reason < ABC =
That angle GEF is similar to triangle DEC?
angles can only be "congruent" (or not!) to other angles. but you should have learned about this fact: |dw:1437055059934:dw|
if you have an "x", the angles opposite each other are congruent (equal to each other) Notice that is also true |dw:1437055171801:dw|
Look at your problem. what angle is a vertical angle to angle CED ?
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 =
I messed up the name of the angle. Better fix it Statement Reason < ABC =
Well, i think that angle ABC and Angle GEF are congruent.. But not sure by which property it is proven.
"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)
Okay.. So i would put that as:
so now the proof is Statement Reason < ABC =
That would be it, right?
now we can add the other given statement
mmm...Im guessing here so i might be wrong... Angles ABC and Angle GFE have corresponding angles? im not sure
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
"Angle GEF is congruent to Angle DEC?"
Is that what they say? read it carefully
They write: In the figure below, .... yes it is
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)?
Angle GFE ≅ ∠DCE..... Idk by which reason.
By which reason??
yes, that is good. the reason is because we were told.
Thank you so much Phi! I appreciate it so very much <3
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 =
< DCE = what other angle ?
what angle is a vertical angle of
when you write down an angle, the "middle" letter is at the vertex so you would write
can you write the next statement in the proof?
Angle DCE = ACB by vertical angles?
Statement Reason < ABC =
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
Thank you so so much! Sorry for leaving, my computer has been crashing a lot lately.