Similarity Criteria Math Example 5

Solution

1. 1
   Step 1: Check the included angle: $\angle Q = \angle T = 50°$. These are the angles between the given sides.
2. 2
   Step 2: Check side ratios around the equal angle: $\frac{PQ}{ST} = \frac{8}{6} = \frac{4}{3}$ and $\frac{QR}{TU} = \frac{12}{9} = \frac{4}{3}$.
3. 3
   Step 3: Both ratios are equal and the included angles are equal, so by SAS~ (Side-Angle-Side Similarity), $\triangle PQR \sim \triangle STU$.
4. 4
   Step 4: The scale factor is $\frac{4}{3}$ (triangle $PQR$ is $\frac{4}{3}$ times the size of triangle $STU$).