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Answer :
To determine whether the pool STUV is similar to pool WXYZ, we can use geometric transformations. Here's a step-by-step explanation of how to do this:
1. Translation: Begin by translating the pool WXYZ so that point W of WXYZ coincides with point S of STUV. This ensures that the two shapes are aligned at one point.
2. Second Translation: Next, translate WXYZ again, this time aligning point X of WXYZ with point T of STUV. By aligning two points, we start the process of matching up the shapes in a way that allows us to compare their sizes.
3. Dilation: Finally, dilate the pool WXYZ by the ratio of the length of segment [tex]\(TS\)[/tex] (from STUV) over the length of segment [tex]\(XW\)[/tex] (from WXYZ). This step adjusts the size of WXYZ so that its corresponding sides are proportional to those of STUV.
By performing these transformations, you change the position and scale of WXYZ. For two shapes to be similar, they must have corresponding angles that are equal and corresponding sides that are proportional. The translation aligns points, while dilation adjusts for proportionality. If after these transformations the shapes have corresponding sides that remain proportionate, then the pools are similar.
1. Translation: Begin by translating the pool WXYZ so that point W of WXYZ coincides with point S of STUV. This ensures that the two shapes are aligned at one point.
2. Second Translation: Next, translate WXYZ again, this time aligning point X of WXYZ with point T of STUV. By aligning two points, we start the process of matching up the shapes in a way that allows us to compare their sizes.
3. Dilation: Finally, dilate the pool WXYZ by the ratio of the length of segment [tex]\(TS\)[/tex] (from STUV) over the length of segment [tex]\(XW\)[/tex] (from WXYZ). This step adjusts the size of WXYZ so that its corresponding sides are proportional to those of STUV.
By performing these transformations, you change the position and scale of WXYZ. For two shapes to be similar, they must have corresponding angles that are equal and corresponding sides that are proportional. The translation aligns points, while dilation adjusts for proportionality. If after these transformations the shapes have corresponding sides that remain proportionate, then the pools are similar.
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