8.2 Similar Polygons
Notes
Similar polygons ($\sim$) have the same shape: corresponding angles are congruent and corresponding sides are proportional.
- The scale factor is the ratio of corresponding sides.
- Ratio of perimeters equals the scale factor $k$.
- Ratio of areas equals $k^2$. (Ratio of volumes of similar solids is $k^3$.)
- Example: $\triangle ABC \sim \triangle DEF$ with $AB = 6$ and $DE = 9$. The scale factor from $ABC$ to $DEF$ is $\displaystyle \frac{3}{2}$.
Practice
$ABCD \sim WXYZ$. $AB = 8$, $WX = 12$ and $BC = 10$. Find $XY$.
Scale factor $\displaystyle \frac{12}{8} = 1.5$, so $XY = 1.5 \cdot 10 = 15$.
Two similar triangles have a scale factor of $2:5$. The smaller has a perimeter of 18. What is the larger perimeter?
Perimeters follow the scale factor: $\displaystyle 18 \cdot \frac{5}{2} = 45$.
Two similar rectangles have a scale factor of $1:3$. The smaller has an area of 10. What is the larger area?
Areas scale by $k^2 = 9$, so $10 \cdot 9 = 90$.
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