Question

Which polygons are similar?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

@izuru

Answer 6

@mathstudent55

Answer 7

@mathway

Answer 8

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

Answer 9

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

Answer 10

@izuru

Answer 11

@izuru ?

Answer 12

@mathstudent55

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

@mathstudent55 ??

Answer 18

please @madhu.mukherjee.946 help or @mathstudent55

Answer 19

i have already told you

Answer 20

ok so i'm thinking D

Answer 21

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

Answer 22

well the only ones that are really similar is D

Answer 23

Let's look at the first choice.

Is 6/7 = 2/3? No, not even close, so eliminate choice A.

Answer 24

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.

Answer 25

ive been saying D -_-

Answer 26

its d

Answer 27

but thank you very much @izuru

Answer 28

Choice B.

Is 15/9 = 35/21 ?

Let's reduce both fractions: 5/3 = 5/3 Yes, it works.
Choice B works.

Answer 29

Choice C.

Is 12/18 = 24/30 ?

Reducing, we get: 2/3 = 4/5. Not true. Choice C does not work.

Answer 30

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.

Answer 31

okay

Answer 32

thanks

Answer 33

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.

Answer 34

You're welcome.