Challenge! Ready? What similarity statement can you write relating the three triangles in the diagram?
http://assets.openstudy.com/updates/attachments/55add702e4b071e6530cdb57-lollygirl217-1437458025655-as.jpg

- anonymous

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- anonymous

This one is really easy~~

- mathstudent55

In a right triangle, when the altitude is drawn to the hypotenuse, the three triangles formed are similar.

- anonymous

Indeed.

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## More answers

- anonymous

Ignore this

##### 1 Attachment

- anonymous

anyone?

- mathstudent55

triangle ABC ~ triangle ADB ~ triangle BDC

- anonymous

That is not right

- mathstudent55

There are 6 correct ways of writing a similarity statement between two triangles.
I wrote one that is correct. There are 5 more correct ones. Just because mine is not the one you expected, it does not mean it's incorrect.

- anonymous

True; but it has to be the one that I posted. Did you look at my shape?

- anonymous

It has to relate to those letters

- mathstudent55

You are missing the point.
With any two given similar triangles, you can write the similarity statement 6 different ways, and they are all correct. The similarity statement I wrote is correct for the figure you posted in the problem. There are 5 more that are also correct.
I wrote a similarity statement relating the three triangles as the problem above asked for. I didn't use x or y or the numbers because that is for a proportion of side lengths. That is not what the problem asks for.

- anonymous

There is one answer and that is not it; that's all I have to say.

- triciaal

IGH = HGF=IHF
= means similar

- anonymous

That is not in the right order

- triciaal

what @mathstudent55 has is correct.

- triciaal

the question is not specific enough if you are expecting one particular answer.

- anonymous

I am expecting one.

- triciaal

do you want the values of x and y?

- anonymous

What he is saying is correct so far

- anonymous

No. What sides are congruent to one another?

- anonymous

What similarity statement can you write relating the three triangles in the diagram?

- anonymous

It really isn't that hard. It's either going to begin with GHF or HIF

- anonymous

or GFH

- mathstudent55

Oh, I see. I used the triangles in the other figure.
Why did you post a figure that is not part of this problem?

- anonymous

I am going to use that for a different question.....I did say to ignore it on top of the pic. Sorry if that threw you off

- mathstudent55

Ok, for the figure with triangle FHI, etc. this is the similarity statement:
triangle FHI ~ triangle FGH ~ triangle HGI

- mathstudent55

Of course, that is one of 6 possible correct similarity statements.

- anonymous

And there is one correct answer for this.

- mathstudent55

No, there are 6 correct answers.

- anonymous

I get what you are saying but there is one that I am looking for.

- mathstudent55

GHF ~ GIH ~ HIF

- anonymous

Correct!

- mathstudent55

Wow, I feel so honored that you approve.
Thanks, and thanks for the medal.

- anonymous

No prob!

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