Which theorem or postulate justifies that angle HEF~angle HGE ?
options and picture of diagram below.

- jaylelile

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- jaylelile

##### 1 Attachment

- jaylelile

A.
AA similarity postulate
B.
SAS similarity theorem
C.
SSS similarity theorem
D.
SSA similarity theorem
I have ruled out option C but I'm stuck now....

- jaylelile

help anyone? I'm totally blank.

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## More answers

- jaylelile

@Concentrationalizing you got anything?

- jaylelile

Is it option A?

- anonymous

I'm pretty new to geometry, honestly. I know a lot of random things about it and can help in certain cases, but I'm taking a geometry course starting in July, so my geometry skills aren't incredibly sound. I was looking in my textbook to get an idea, actually xD I mean, clearly they're similar, but I havent learned all the postulates and theorems yet. But I was taking a look at the question because I need to familiarize myself with as much of it as possible for when I take the course.

- jaylelile

aaaaaah.
Thanks anyway!

- anonymous

Everything I see has to do with showing that triangles are similar. And all of those ideas use the congruency of angles. I dont see any mention about saying angles are similar, only that triangles are similar. I was thinking that maybe its supposed to be
∠HEF ≅ ∠ HGE ? Congruence of the angles as opposed to similarity of them?

- anonymous

you can find out angle E for the right triangle by subtracting 90 plus 53 from 180

- anonymous

then you should have an option

- jaylelile

wait but I don't need to find out angle E do I? I just need to know what postulate/theorem justifies the angles? I'm so confused.

- welshfella

not sure which postulate is correct but i know that triangles EHF and GEF are similar

- anonymous

So, here's what I'm thinking:
I don't believe A is the correct choice. We're trying to prove that ∠HEF ≅ ∠ HGE. Now, we can do some simple math and find those angles but I dont think we're allowed to do that in this problem, it defeats the purpose of the proof. From what I see, AA postulate requires that we already know two angles are congruent. I don't think we can obtain that knowledge without breaking the rules of the proof.
As you said, I wouldnt expect C to be correct either. Even though we can make a logical inference from it, all SSS does is prove triangles are similar using sides, but not angles.
I don't even see an SSA similarity postulate in my textbook, only SAS. So I would reason that answer B is correct. We can use pythagorean theorem to find the sides of the triangle and we already know that we have one congruent angle, the 90 degree one.

- anonymous

I dont think finding angle E is really allowed in what we're doing. I would expect that we need to do anything else EXCEPT find those angles. We're not supposed to assume that knowledge. But I could be completely wrong, its just my reasoning

- welshfella

similar traingles are the same shape - that is the corresponding angles are equal

- welshfella

IF AA means that 2 angles can be shown to be equal then the other angles must also be eqqual so I would guess that A is the correct option.

- jaylelile

So option B? I think that would make the most sense. Unless this is a trick question...

- jaylelile

wait why option A????? I'm so lost!

- anonymous

Well, AA proves triangles are similar. But the main question I would have is can we make an indirect conclusion? Showing that the triangles are similar would definitely imply the angles are congruent, but we could use multiple options to show the similarity of the triangles.

- welshfella

S means equal sides - that is used for congruent ( exactly the same ) triangles . It must be A.

- anonymous

We're working with similarity postulates though, which have to do with the ratio of corresponding sides of a triangle, not the equality of corresponding sides.

- welshfella

No - all we need do is prove that 2 angles are congruent.

- jaylelile

A is a similarity postulate. I do think that it might be correct now it's making more sense.

- anonymous

Im not trying to argue Im right and anyone is wrong, Im just stating my arguments and trying to learn, so I just wanted to clarify that, lol.

- jaylelile

no no @Concentrationalizing this isn't turning into an argument, just a discussion. I do appreciate everyone's insight and help a ton!

- anonymous

I know it isnt an argument, I just want to make sure that no-one thinks it is :)

- welshfella

- welshfella

Yes A is definitely correct. We don't have this naming convention in the UK - thats whyI was a bit puzzled , at first.

- welshfella

SSS must be 3 sides equal which shows that the triangles are congruent

- jaylelile

welshfella is definitely making sense to me, I agree it must be A. Thank you so much!!!!!!

- welshfella

SAS and - 2 sides and the included angle - congruent triangles

- anonymous

I still think you're mixing up similarity and congruence. The SSS you're speaking of is SSS congruence postulate. But the options are specifically similarity postulates, not congruence.

- welshfella

congruent triangles are also similar of course but in this problem the triangles are obviously not congruent

- anonymous

Okay, so one question before I mention what issues Im having. Is the strategy you're using to show that the similarity of triangles implies the congruence of the angles?

- welshfella

the congruence of the angles implies the similarity of the triangles.

- anonymous

Aren't we trying to show the congruence of the angles, though? Not the similarity of the triangles? It sounds like that'd be going in the opposite direction.

- jaylelile

congruence and similarity is the same thing.

- jaylelile

well pretty much anyway.

- anonymous

Well they aren't the same nor are the theorems. But I know there's something I'm missing behind the reasoning. Otherwise I could just explain my concerns and see why I may be wrong xD

- welshfella

no - not really when we talk about similar triangles in Geometry we mean triangles with the same shape but different side lengths.

- welshfella

I must admit I'm a little confused about the word similarity in the mentioned postulates
SSS would be equated to congruence.

- anonymous

I just want to make clear what you're trying to do when determining this. So you said the congruence of angles implies the similarity of the triangles, which I perfectly agree. But I think that statement is in the reverse direction of what we want. The final result is that we want the congruence of the angles, so I wouldnt think we could try to do anything but show that the congruence of the angles is implied by something else.

- welshfella

Yes but to find the congruence of the angles in the question we do it by proving the similarity of the 2 triangles. And we do this by proving that the other 2 angles in ecah triangles are congruent.

- welshfella

= thats why I think the AA postulate is the correct one.

- anonymous

Okay, here's what I have in my textbook about it, Welsh:
"Side-side-side (SSS) Congruence Postulate:
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent."
That's the congruence one. Now there is an SSS similarity one as well, however
"Side-side-side (SSS) Similarity Theorem:
If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar."
As in:
|dw:1433541678140:dw|

- welshfella

Ah - I see what they mean - Yes thats another way to show that triangles are similar - if the sides are in same proportion
I understand that now.

- anonymous

Correct. And because of that, it seemed like there would be multiple ways to show what we need to show. Pythagorean theorem let's us get all the required side lengths and their proportions, which would show similar triangles and then imply the congruence of the angles. So it almost seems like you could claim A, B, and C could be correct, I was just trying to figure out which one would be the "most correct".

- welshfella

well I think the AA postulate is correct for one but yes there could be others which are correct as well

- welshfella

the side GF in the large triangle is 50 by pythagoras

- anonymous

Yeah, I also notice that you're considering the entire larger triangle where I was only considering the two individual triangles. I'm considering it now from the large triangle.

- anonymous

Yeah, I guess when you consider it from the larger triangle, AA makes a lot of sense.

- welshfella

30 / 50 = 24/40
- these lines are from large triangle and the smallest one
- that is enough to show that they are similar - also the angle 53 degrees is common so is that the SSA or SAS postulate?

- welshfella

i must admit I find this confusing and I wonder if they are really necessary..

- anonymous

I dont even show an SSA postulate in my text when it comes to similarity, only when it comes to congruence. Im not sure that one exists, I think its just a trick answer.

- welshfella

yes - could be

- anonymous

Yeah, exactly. They dont seem necessary and they pretty much all seem sufficient to come to the conclusion on their own.

- anonymous

But when you consider the larger triangle and not just the two independent smaller triangles, it seems like you can come to the most direct conclusion, where it seems like the others require some more calculation or an indirect result.

- welshfella

i need to turn in now - its been interesting talking to you.
Good luck!

- welshfella

yes

- anonymous

Alright, thanks for the conversation, much appreciated :)

- welshfella

I was wrong when I said that two side.s in same. Ratio prove that the trIangles are similar you need an equal angle as ,well,
I have. Read up on this and I've the a sass and says postulate but not the S.s,a As you said.

- welshfella

* SAS and SSS postulates

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