Question

Are the two triangles below similar?
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Yes; they have congruent corresponding angles
No; they do not have congruent corresponding angles
Yes; they have proportional corresponding sides
No; they do not have proportional corresponding sides

Answer 1

@CaptainFluffy

Answer 2

same angles diff size

Answer 3

The way I figure it, the angle that's measured 27 on both triangles is congruent (it's in the same place on each and the same measurement). The angle that's measured 108 on the small triangle is not marked on the bigger triangle, so I don't know if that's congruent to the corresponding angle there. Same goes for the angle on the big triangle that's marked 46.

Answer 4

>same angles

They are not the same so the AA Similarity Postulate does not hold.

Answer 5

So I think the angle marked 27 is corresponding and congruent, but the others are unknown

Answer 6

Compute the sizes of <H and <J.

Answer 7

the others are known, 108 and 46

Answer 8

Directrix, how would I do that? Or can I?

Answer 9

But, are two angles of one triangle congruent to two angles of the other?

Answer 10

Now, similarity in difference with congruence does not imply equality but proportionality.
We can define similarity of two triangles \(\triangle ABC\) and \(\triangle xyz \) with the following mathematical structure: \[\frac{ xy }{ AB } =\frac{ xz }{ AC }=\frac{ yz }{ CB }=k\]
indeed, we can define this more simply by saying that the division of their corresponding sides must give as a result a constant "k" which is called "coefficient of proportionality".
From this definition we stem a very important rule of similarity, wich is denominated \(AAA\) (Angle-Angle-Angle) which states that if we have two triangles in the plane and their angles all have the same measure, we can conclude that they are similar, thereby, the mathematical representation being:
\(\triangle ABC\) and \(\triangle xyz\)
\(\angle A=\angle x\), \(\angle B = \angle y\) , \(\angle C = \angle z\)
\[\rightarrow \triangle ABC \sim \triangle xyz \]

A triangles angles sum up to 180º, thefore, o nthe two triangles on your geometry problem can be solved for the missing angle using this property, if al lthe angle show to be the same, the theorem of similarity can be applied to assure their similarity.

Answer 11

directrix knows more then i do, its all yours diretrix

Answer 12

WOW so owl coffee was actually typing and not getting his triple mocha decaf lol

Answer 13

Oh, that makes a lot of sense to me actually, Owl.
Thanks for taking the time to write all of that.

Answer 14

I am the type of person who dislikes to skip details, if you have any further questions about this problem, don't hesitate :)

Answer 15

Thank you so much!

Answer 16

Okay, so I understand the "all triangles equal 180" basic statement, but I get a bit confused because I can apply it to this question and figure out the missing angle but I still can't figure how any of it applies to the answer choices.

Answer 17

>>Directrix, how would I do that? Or can I?

Add the two angles with given measures in a triangle and subtract from 180.

The sum of the interior angles of a triangle is 180.

Answer 18

Okay, so I can do that. But how does that apply to the answer choices?

Answer 19

The answer options are slightly odd.

This is my best bet at the correct answer:

No; they do not have congruent corresponding angles

Answer 20

For the triangle to be similar, the angles have to be the same in each to give the triangles the same shape.

Answer 21

Okay, thank you for clarifying that.

Answer 22

You are welcome.