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misssunshinexxoxo
 one year ago
Best ResponseYou've already chosen the best response.0Don't you see that abc and gfe are congruent?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But with which property do i prove that with?

misssunshinexxoxo
 one year ago
Best ResponseYou've already chosen the best response.0You should write out a proof for this.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, but im not really good at this, could you walk me through it?

misssunshinexxoxo
 one year ago
Best ResponseYou've already chosen the best response.0Sure review this https://www.wyzant.com/resources/lessons/math/geometry/triangles/angles_of_triangles

phi
 one year ago
Best ResponseYou've already chosen the best response.3Here is what the first sentence tells us < ABC = <DEC

phi
 one year ago
Best ResponseYou've already chosen the best response.3write that statement and next to it write the reason we know it is true. Do you know the reason?

phi
 one year ago
Best ResponseYou've already chosen the best response.3We are told it is true. the short reason is " given "

phi
 one year ago
Best ResponseYou've already chosen the best response.3so the first line of your proof should read Statement Reason < ABC = <DCE Given

phi
 one year ago
Best ResponseYou've already chosen the best response.3<DCE is not part of the triangle we are interested in (the question asks us to prove triangle ABC is similar to triangle GEF.. which means show "corresponding angles" are equal ) However, we can deduce something about angle GEF Any idea what ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That angle GEF is similar to triangle DEC?

phi
 one year ago
Best ResponseYou've already chosen the best response.3angles can only be "congruent" (or not!) to other angles. but you should have learned about this fact: dw:1437055059934:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.3if you have an "x", the angles opposite each other are congruent (equal to each other) Notice that is also true dw:1437055171801:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.3Look at your problem. what angle is a vertical angle to angle CED ?

phi
 one year ago
Best ResponseYou've already chosen the best response.3Yes. 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 = <DCE Given <DCE = <GEF vertical angles

phi
 one year ago
Best ResponseYou've already chosen the best response.3I messed up the name of the angle. Better fix it Statement Reason < ABC = <DEC Given <DEC = <GEF vertical angles

phi
 one year ago
Best ResponseYou've already chosen the best response.3if <ABC = < DEC and <GEF = <DEC any idea about <ABC and <GEF ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, i think that angle ABC and Angle GEF are congruent.. But not sure by which property it is proven.

phi
 one year ago
Best ResponseYou've already chosen the best response.3"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
 one year ago
Best ResponseYou've already chosen the best response.0Okay.. So i would put that as: <ABC = <GEF By the transitivity property?

phi
 one year ago
Best ResponseYou've already chosen the best response.3so now the proof is Statement Reason < ABC = <DEC Given <DEC = <GEF vertical angles <ABC = <GEF transitivity

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That would be it, right?

phi
 one year ago
Best ResponseYou've already chosen the best response.3now we can add the other given statement

phi
 one year ago
Best ResponseYou've already chosen the best response.3can you add that next line? Here is the picture (I tried to add a blue line showing the two angles )

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0mmm...Im guessing here so i might be wrong... Angles ABC and Angle GFE have corresponding angles? im not sure

phi
 one year ago
Best ResponseYou've already chosen the best response.3Read 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
 one year ago
Best ResponseYou've already chosen the best response.0"Angle GEF is congruent to Angle DEC?"

phi
 one year ago
Best ResponseYou've already chosen the best response.3Is that what they say? read it carefully

phi
 one year ago
Best ResponseYou've already chosen the best response.3They write: In the figure below, .... yes it is <GFE and what is the other angle?

phi
 one year ago
Best ResponseYou've already chosen the best response.3yes, 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
 one year ago
Best ResponseYou've already chosen the best response.0Angle GFE ≅ ∠DCE..... Idk by which reason.

phi
 one year ago
Best ResponseYou've already chosen the best response.3yes, that is good. the reason is because we were told.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much Phi! I appreciate it so very much <3

phi
 one year ago
Best ResponseYou've already chosen the best response.3yes, 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 = <DEC Given <DEC = <GEF vertical angles <ABC = <GEF transitivity <GFE ≅ ∠DCE Given any idea what to do next ?

phi
 one year ago
Best ResponseYou've already chosen the best response.3< DCE = what other angle ?

phi
 one year ago
Best ResponseYou've already chosen the best response.3what angle is a vertical angle of <DCE ? (the other side of the "x" )

phi
 one year ago
Best ResponseYou've already chosen the best response.3when you write down an angle, the "middle" letter is at the vertex so you would write <ACB or <BCA

phi
 one year ago
Best ResponseYou've already chosen the best response.3can you write the next statement in the proof? <DCE = ??? what reason?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Angle DCE = ACB by vertical angles?

phi
 one year ago
Best ResponseYou've already chosen the best response.3Statement Reason < ABC = <DEC Given <DEC = <GEF vertical angles <ABC = <GEF transitivity <GFE ≅ ∠DCE Given <DCE = <ACB vertical angles notice we can now write <GFE= <ACB what is the reason ?

phi
 one year ago
Best ResponseYou've already chosen the best response.3the 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
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so so much! Sorry for leaving, my computer has been crashing a lot lately.
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