Challenge! Ready? Are the polygons similar? If they are, write a similarity statement and give the scale factor. The figure is not drawn to scale.

- anonymous

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- anonymous

##### 1 Attachment

- anonymous

If they are, tell me the reason why. Hint, what sides go together? What ratio?

- anonymous

That is the key to knowing ;)

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## More answers

- triciaal

do you see any angles that are the same?

- triciaal

are the corresponding sides in the same ratio?

- mathstudent55

Polygons are similar if the following two conditions are met:
1. All angles of one polygon are congruent to the corresponding angles of the other polygon.
2. All pairs of corresponding sides have the same ratio of lengths.

- mathstudent55

If you can meet those conditions they are similar.

- anonymous

Indeed.

- anonymous

Whoever gets the answer will win~!

- mathstudent55

Look at the polygons.
One has sides 6, 6, 2.8, 2.8
The other has sides 4.5, 4.5, 2.1, 2.1
Since in each polygon, each pair of opposite sides is congruent, both polygons are parallelograms.

- anonymous

mhm

- anonymous

Agreed

- mathstudent55

In a parallelogram, opposite angles are congruent.
That means each polygon has opposite angles measuring 110 degrees and another pair of opposite angles measuring 70.
That means the corresponding congruent angles are present.

- anonymous

You are correct about the decimals!

- anonymous

What sides go together?

- mathstudent55

Since you agree, and it seems you really know about this, I'll let you finish.

- anonymous

Hopefully no one says the answer before you

- mathstudent55

I'm hoping you tell me the answer. I'd like to hear it from you.

- anonymous

Why would I tell? It is a challenge

- anonymous

Whoever answers correctly wins the medal

- anonymous

You got it right so far

- anonymous

Begins with T

- anonymous

another hint....after that is U

- anonymous

Who will get it?

- mathstudent55

No more hints?

- anonymous

You need more professor?

- triciaal

don't need a medal. you already know they are similar. DGE = VTU

- anonymous

That is not it.

- anonymous

Here: The first four are TUWV=??

- anonymous

What is congruent to those?

- triciaal

scale factor 3/4

- anonymous

What is congruent to those? Thats all that needs to be solved, too bad that professor is not here

- triciaal

defg

- anonymous

That is correct. But since you are different person; actually. You also have to tell me the decimals

- anonymous

/ratio

- anonymous

Ignore this

##### 1 Attachment

- anonymous

Anyone??

- anonymous

wb mathstudent, looks like you are going to be the winner

- mathstudent55

To finish, you must look at the ratios of the lengths of the sides:
\(\dfrac{6}{4.5} = \dfrac{4}{3} \)
\(\dfrac{2.8}{2.1} = \dfrac{4}{3} \)
The ratios of the corresponding sides are equal, so the quadrilaterals are similar.
Now we need to write the correct statement of similarity.

- mathstudent55

quadrilateral TUWV ~ quadrilateral DEFG

- anonymous

Correct

- mathstudent55

thanks

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