anonymous
  • anonymous
Which polygons are similar?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
http://static.k12.com/calms_media/media/1421000_1421500/1421034/1/9f9ab2b63740c2539d852f3b9058a3d09d40aa64/MS_Alg_130924_281846.jpg
anonymous
  • anonymous
http://static.k12.com/calms_media/media/1421000_1421500/1421035/1/a6667e6f57ca5de7bd1301bb8c95f6dc35ad8f1c/MS_Alg_130924_281847.jpg
anonymous
  • anonymous
http://static.k12.com/calms_media/media/1421000_1421500/1421036/1/accef9e31e5fbe66b37ae4a30771bd36c4e3782a/MS_Alg_130924_281848.jpg

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anonymous
  • anonymous
http://static.k12.com/calms_media/media/1421000_1421500/1421037/1/1f05837e50837ce7827ad555460aa9985f7f6cc3/MS_Alg_130924_281849.jpg
anonymous
  • anonymous
@izuru
anonymous
  • anonymous
@mathstudent55
anonymous
  • anonymous
@mathway
anonymous
  • anonymous
Try to figure out the proportion of all the two pairs of polygons first.
anonymous
  • anonymous
8 and 10 for first 50 and 30 for 2nd 36 and 48 for 3rd 21 and 30 for the 4th
anonymous
  • anonymous
@izuru
anonymous
  • anonymous
@izuru ?
anonymous
  • anonymous
@mathstudent55
mathstudent55
  • mathstudent55
Do you know what is needed for two polygons to be similar?
anonymous
  • anonymous
no but i just need to get this done quick its been 10 minutes all ready. :(
mathstudent55
  • 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
  • madhu.mukherjee.946
If two polygons are similar, then the ratio of the lengths of the two corresponding sides is the scale factor.
anonymous
  • anonymous
@mathstudent55 ??
anonymous
  • anonymous
please @madhu.mukherjee.946 help or @mathstudent55
madhu.mukherjee.946
  • madhu.mukherjee.946
i have already told you
anonymous
  • anonymous
ok so i'm thinking D
madhu.mukherjee.946
  • madhu.mukherjee.946
you go to check both the polygons and see if they are similar based on the the two conditiond
anonymous
  • anonymous
well the only ones that are really similar is D
mathstudent55
  • mathstudent55
Let's look at the first choice. Is 6/7 = 2/3? No, not even close, so eliminate choice A.
anonymous
  • 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
  • anonymous
ive been saying D -_-
madhu.mukherjee.946
  • madhu.mukherjee.946
its d
anonymous
  • anonymous
but thank you very much @izuru
mathstudent55
  • mathstudent55
Choice B. Is 15/9 = 35/21 ? Let's reduce both fractions: 5/3 = 5/3 Yes, it works. Choice B works.
mathstudent55
  • mathstudent55
Choice C. Is 12/18 = 24/30 ? Reducing, we get: 2/3 = 4/5. Not true. Choice C does not work.
mathstudent55
  • 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
  • madhu.mukherjee.946
okay
madhu.mukherjee.946
  • madhu.mukherjee.946
thanks
mathstudent55
  • 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
  • mathstudent55
You're welcome.

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