gen-define-similar-triangles-and-give-one-short-worked-example-6bf6

Define similar triangles and give one short worked example.

# Similar Triangles **Definition:** Two triangles are **similar** if they have the same shape but not necessarily the same size. This means: - All corresponding angles are equal - All corresponding sides are in the same ratio (proportional) We write △ABC ~ △DEF to show triangles ABC and DEF are similar. --- ## Worked Example **Given:** △ABC ~ △DEF with AB = 6 cm, BC = 8 cm, and DE = 9 cm. **Find:** EF **Solution:** Since the triangles are similar, corresponding sides are proportional: $$\frac{AB}{DE} = \frac{BC}{EF}$$ $$\frac{6}{9} = \frac{8}{EF}$$ Cross-multiply: $$6 \times EF = 9 \times 8$$ $$6 \times EF = 72$$ $$EF = 12 \text{ cm}$$ The scale factor is 9/6 = 3/2, so EF = 8 × (3/2) = 12 cm.