Questions: BCDEF ~ TUVWS. Find TU. T U=

Transcript text: BCDEF ~ TUVWS. Find TU. \[ T U= \]

Solution

Solution Steps

Step 1: Identify corresponding sides

The problem states that BCDEF ~ TUVWS. This means that the polygons are similar, and their corresponding sides are proportional. The corresponding sides are: BC and TU CD and UV DE and VW EF and WS FA and ST

Step 2: Set up a proportion

We are given that BC = 4, CD = 12, and EF = 4. We are asked to find TU. Since the polygons are similar, we can set up a proportion using the ratio of corresponding sides: \( \frac{BC}{TU} = \frac{EF}{WS} \)

Step 3: Substitute known values

Substitute the given values into the proportion: \( \frac{4}{TU} = \frac{4}{WS} \)

Step 4: Solve for TU

Notice that the numerator on both sides is 4. This means that TU = WS. Although we do not know the value of WS, we can infer from the proportion that TU must equal BC, as the ratio of their corresponding sides must be the same as the ratio of EF to WS. In this case, since the ratio of EF and WS is 1, the ratio of BC and TU must also be 1, resulting in TU = BC = 4.

Final Answer

\\(\boxed{TU=4}\\)

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