Which polygons are similar?

- anonymous

Which polygons are similar?

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- schrodinger

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- anonymous

http://static.k12.com/calms_media/media/1421000_1421500/1421034/1/9f9ab2b63740c2539d852f3b9058a3d09d40aa64/MS_Alg_130924_281846.jpg

- anonymous

http://static.k12.com/calms_media/media/1421000_1421500/1421035/1/a6667e6f57ca5de7bd1301bb8c95f6dc35ad8f1c/MS_Alg_130924_281847.jpg

- anonymous

http://static.k12.com/calms_media/media/1421000_1421500/1421036/1/accef9e31e5fbe66b37ae4a30771bd36c4e3782a/MS_Alg_130924_281848.jpg

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## More answers

- anonymous

http://static.k12.com/calms_media/media/1421000_1421500/1421037/1/1f05837e50837ce7827ad555460aa9985f7f6cc3/MS_Alg_130924_281849.jpg

- anonymous

@izuru

- anonymous

@mathstudent55

- anonymous

@mathway

- anonymous

Try to figure out the proportion of all the two pairs of polygons first.

- anonymous

8 and 10 for first 50 and 30 for 2nd 36 and 48 for 3rd 21 and 30 for the 4th

- anonymous

@izuru

- anonymous

@izuru ?

- anonymous

@mathstudent55

- mathstudent55

Do you know what is needed for two polygons to be similar?

- anonymous

no but i just need to get this done quick its been 10 minutes all ready. :(

- mathstudent55

Two polygons are similar if each pair of corresponding angles is congruent, and if the ratios of the lengths of corresponding sides are equal.

- madhu.mukherjee.946

If two polygons are similar, then the ratio of the lengths of the two corresponding sides is the scale factor.

- anonymous

@mathstudent55 ??

- anonymous

please @madhu.mukherjee.946 help or @mathstudent55

- madhu.mukherjee.946

i have already told you

- anonymous

ok so i'm thinking D

- madhu.mukherjee.946

you go to check both the polygons and see if they are similar based on the the two conditiond

- anonymous

well the only ones that are really similar is D

- mathstudent55

Let's look at the first choice.
Is 6/7 = 2/3? No, not even close, so eliminate choice A.

- anonymous

Okay so all the proportions are:
rectangle:
\[\[\frac{ 7 }{ 6 }=\frac{ 2 }{ 3 }\]\]
right triangle:
\[\frac{ 9}{ 15 }=\frac{ 21 }{ 35 }\]
trapezoid:
\[\frac{ 12 }{ 18 }=\frac{ 24 }{ 30 }\]
isoceles:
\[\frac{ 12}{ 9 }=\frac{ 12 }{ 9 }\]
Figure out which ones are congruent.

- anonymous

ive been saying D -_-

- madhu.mukherjee.946

its d

- anonymous

but thank you very much @izuru

- mathstudent55

Choice B.
Is 15/9 = 35/21 ?
Let's reduce both fractions: 5/3 = 5/3 Yes, it works.
Choice B works.

- mathstudent55

Choice C.
Is 12/18 = 24/30 ?
Reducing, we get: 2/3 = 4/5. Not true. Choice C does not work.

- mathstudent55

Choice D.
Is 12/9 = 12/9 = 6/3 ?
Reducing we get:
4/3 = 4/3 = 2/1. Not true. Choice also does not work.
The only answer is Choice B.

- madhu.mukherjee.946

okay

- madhu.mukherjee.946

thanks

- mathstudent55

In choice A, we are given two quadrilaterals.
All angles are right angles, so we know they are rectangles.
Since rectangles are parallelograms, opposite sides are congruent.
Checking the length ratios of two pairs of adjacent sides, that is enough to know whether they are or are not similar. In this case, they were not.
In choice B, we deal with triangles. We are given the lengths of two pairs of sides and their included angles. Since the sides were of proportional length, and the included angles were congruent, then by SAS Similarity, the triangles are similar.
In choice C, we have quadrilaterals again. We are given two pairs of sides. We assume those sides were corresponding. It turned out their lengths were not proportional, so we can say the quadrilaterals are not similar. The problem here is that even if the side lengths had turned out to be proportional, we would not be able to conclude the quadrilaterals are similar because we don't know about the other 2 of pairs of angles or the other two pairs of sides.
In choice D, we were given two triangles and the lengths of all six sides. If every pair of corresponding sides were in the same ratio, then by SSS Similarity, we would be able to conclude the triangles are similar, but only 2 pairs of sides were in the same ratio. The third pair of sides is not, so the triangles are not similar.

- mathstudent55

You're welcome.

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