Similarity Criteria Math Example 3

Solution

1. 1
   Step 1: Order the sides of each triangle from smallest to largest. $\triangle ABC$: $5, 12, 13$. $\triangle DEF$: $10, 24, 26$.
2. 2
   Step 2: Compute the ratios of corresponding sides: $\dfrac{10}{5} = 2$, $\dfrac{24}{12} = 2$, $\dfrac{26}{13} = 2$.
3. 3
   Step 3: All three ratios are equal ($k = 2$), so every pair of corresponding sides is proportional.
4. 4
   Step 4: By SSS~ (Side-Side-Side Similarity), $\triangle ABC \sim \triangle DEF$ with scale factor $2$.