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Answer :
To determine whether pool STUV is similar to pool WXYZ, we'll compare their shapes and ensure one can be transformed into the other through a combination of translations and dilations. Here's how we can approach this:
1. Translation: Start by translating pool WXYZ so that one of its points, specifically point W, lies on the corresponding point S of pool STUV. This step aligns the two pools at one corner, making sure they start at the same point.
2. Dilation: After translation, we need to resize pool WXYZ to check for similarity. Perform a dilation (a resizing operation) on pool WXYZ with respect to the aligned points. In this case, dilate WXYZ by the ratio [tex]\(\frac{\overline{TS}}{\overline{XW}}\)[/tex].
- This means you adjust the size of pool WXYZ by the ratio of the corresponding side lengths from STUV and WXYZ. The sides TS and XW correspond because they are both the first sides mentioned in the question.
3. Verification: After translation and dilation, pool WXYZ should now cover pool STUV perfectly if they are similar. If every corresponding point and side lines up, pool STUV and WXYZ are indeed similar.
In conclusion, the most effective method involves translating WXYZ so point W aligns with S, followed by dilating WXYZ by the ratio of the corresponding side lengths, [tex]\(\frac{\overline{TS}}{\overline{XW}}\)[/tex]. This ensures that WXYZ fits perfectly on STUV, proving their similarity.
1. Translation: Start by translating pool WXYZ so that one of its points, specifically point W, lies on the corresponding point S of pool STUV. This step aligns the two pools at one corner, making sure they start at the same point.
2. Dilation: After translation, we need to resize pool WXYZ to check for similarity. Perform a dilation (a resizing operation) on pool WXYZ with respect to the aligned points. In this case, dilate WXYZ by the ratio [tex]\(\frac{\overline{TS}}{\overline{XW}}\)[/tex].
- This means you adjust the size of pool WXYZ by the ratio of the corresponding side lengths from STUV and WXYZ. The sides TS and XW correspond because they are both the first sides mentioned in the question.
3. Verification: After translation and dilation, pool WXYZ should now cover pool STUV perfectly if they are similar. If every corresponding point and side lines up, pool STUV and WXYZ are indeed similar.
In conclusion, the most effective method involves translating WXYZ so point W aligns with S, followed by dilating WXYZ by the ratio of the corresponding side lengths, [tex]\(\frac{\overline{TS}}{\overline{XW}}\)[/tex]. This ensures that WXYZ fits perfectly on STUV, proving their similarity.
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