Use the figure below to answer the question that follows:

- anonymous

Use the figure below to answer the question that follows:

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- anonymous

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- anonymous

What must be given to prove that ΔBHG ≅ ΔCHI?
∠GBH ≅ ∠ICH and ∠BGH ≅ ∠CIH
segment BH is congruent to segment CH and segment BG is congruent to segment CI
∠GBH ≅ ∠ICH and ∠BHG ≅ ∠CHI
segment BH is congruent to segment CH and segment HG is congruent to segment HI

- anonymous

I think it's C.

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## More answers

- anonymous

Haha, sorry but I completely suck at math. I'm just here to say welcome back to openstudy!

- anonymous

It's okay, and thanks!

- anonymous

@e.mccormick @nincompoop @mathstudent55

- anonymous

I think its BH congruent to CH and BG to CL. I could be wrong because I never did this before....... ;)

- anonymous

Sorry if I misguide you @ilikemath50

- anonymous

That's okay, thanks for trying! :) @kalahkid

- anonymous

@e.mccormick So, what do you think?

- e.mccormick

AAA all three angles congruent only proves similarity, not congruance.
|dw:1434063901941:dw|

- anonymous

Yeah, I know that. The same goes for SSS, ASA, SAS, and AAS right?

- e.mccormick

You always need to go with all three sides, angle-side-angle, or side-angle-side to prove congruence.

- anonymous

Oh, okay

- anonymous

I didn't know that one.

- e.mccormick

AAS... f I recall, does not always come out congruent.

- e.mccormick

There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.
http://www.mathsisfun.com/geometry/triangles-congruent-finding.html

- e.mccormick

So there is it...

- anonymous

Thank you, but the answer is either B or D? Right?

- anonymous

I'm leaning a little closer to D.

- e.mccormick

Well, they only gibe two sides, so you must use an angle out of the image that must be the same... which means that the rules for angles on crossed lines need to apply.

- e.mccormick

Note it is AAS that is congruent, not SSA.

- e.mccormick

That was the one I was trying to remember that tricks people... SSA.

- e.mccormick

Take this triangle with the marked side, side and angle:
|dw:1434064547599:dw|

- e.mccormick

Now, let me modify it so those are the same, but the triangle is not:
|dw:1434064605461:dw|
If done carefully or with a compass, this can show that SSA/retricetriangles do not prove congruance.

- anonymous

Oh, okay. I'm understanding a bit better now.

- e.mccormick

|dw:1434064707031:dw|

- e.mccormick

Because the radius of the sircle determines one side, a circle can prove that retricemakes for two triangles... That was the proof I was trhying to think of.

- e.mccormick

Anyhow... one of those answers you liked was retrice not SAS.

- e.mccormick

SSA not SAS....

- anonymous

Oh, so it's A?

- e.mccormick

It will never be angles alone. That was the AAA problem. So you need sides. So it was one of the side ones, as you thought.
So which side answer is SAS and which is SSA?

- anonymous

B is SAS
D is SSA

- e.mccormick

segment BH is congruent to segment CH and segment BG is congruent to segment CI
|dw:1434065227574:dw|
segment BH is congruent to segment CH and segment HG is congruent to segment HI
|dw:1434065287345:dw|

- e.mccormick

Do you see it now? I just sketched the parts involved in the answer....

- anonymous

Ohh, I think I'm getting it.

- e.mccormick

|dw:1434065377344:dw|
|dw:1434065436305:dw|

- anonymous

Ugh, I have to go leave my house now. But I think I know the answer, D right?

- e.mccormick

Yah. I hope that the drawings help with remembering why it is D.

- anonymous

Thank you sooooo much!

- e.mccormick

Have fun!

- anonymous

:)

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