Similarity Criteria Math Example 2

Solution

1. 1
   Step 1: Check if corresponding sides are proportional. Set up ratios: $\frac{AB}{DE} = \frac{6}{4} = 1.5$, $\frac{BC}{EF} = \frac{9}{6} = 1.5$, $\frac{AC}{DF} = \frac{12}{8} = 1.5$.
2. 2
   Step 2: All three ratios equal 1.5, so all three pairs of corresponding sides are proportional with scale factor $k = 1.5$.
3. 3
   Step 3: By SSS~ (Side-Side-Side Similarity), if all three pairs of corresponding sides are proportional, the triangles are similar.
4. 4
   Step 4: Conclude: $\triangle ABC \sim \triangle DEF$ by SSS~ with scale factor $\frac{3}{2}$.