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Answer :
To determine if pool STUV is similar to pool WXYZ, we need to check if the pools have the same shape but can be different sizes. Here is how you can verify similarity:
1. Translation: Start by translating (moving) pool WXYZ such that point W of WXYZ aligns with point S of STUV. This ensures the pools are in the same position with respect to one point.
2. Dilation: After translating, you'll need to check if we can adjust the size of WXYZ to match STUV while maintaining shape proportions. This adjustment is called dilation. To do this, you would dilate WXYZ by the ratio of the length of corresponding sides in the pools. Specifically, use the ratio [tex]\(\frac{\overline{TS}}{\overline{XW}}\)[/tex], since TS and XW are the corresponding sides on pools STUV and WXYZ, respectively.
By performing these transformations (translation and dilation), you can determine if pool STUV is indeed similar to pool WXYZ. For two figures to be similar, after positioning one on top of the other, you should be able to enlarge or reduce one figure by a consistent ratio (dilation) to make them coincide exactly with the other. This is the essential process to check for similarity based on geometric transformations.
1. Translation: Start by translating (moving) pool WXYZ such that point W of WXYZ aligns with point S of STUV. This ensures the pools are in the same position with respect to one point.
2. Dilation: After translating, you'll need to check if we can adjust the size of WXYZ to match STUV while maintaining shape proportions. This adjustment is called dilation. To do this, you would dilate WXYZ by the ratio of the length of corresponding sides in the pools. Specifically, use the ratio [tex]\(\frac{\overline{TS}}{\overline{XW}}\)[/tex], since TS and XW are the corresponding sides on pools STUV and WXYZ, respectively.
By performing these transformations (translation and dilation), you can determine if pool STUV is indeed similar to pool WXYZ. For two figures to be similar, after positioning one on top of the other, you should be able to enlarge or reduce one figure by a consistent ratio (dilation) to make them coincide exactly with the other. This is the essential process to check for similarity based on geometric transformations.
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