Questions: Determine whether or not the triangles can be proven similar. If so, state the similarity postulate. ST=9, WT=8, TV=6, and TU=16/3.

Solution Steps

To determine if the triangles can be proven similar, we need to compare the ratios of their corresponding sides. If the ratios are equal, then the triangles are similar by the SSS (Side-Side-Side) similarity postulate.

We are given the following side lengths:

• \( S T = 9 \)
• \( W T = 8 \)
• \( T V = 6 \)
• \( T U = \frac{16}{3} \approx 5.3333 \)

We calculate the ratios of the corresponding sides:

• Ratio 1: \( \frac{S T}{W T} = \frac{9}{8} = 1.125 \)
• Ratio 2: \( \frac{T V}{T U} = \frac{6}{5.3333} \approx 1.125 \)

Since the ratios of the corresponding sides are equal: \[ \frac{S T}{W T} = \frac{T V}{T U} = 1.125 \]

Final Answer