Similarity & Scale
Similar shapes: angles equal, sides in same ratio (scale factor).
\( \text{Scale factor} = \frac{\text{new length}}{\text{original length}} \)
\( \text{Area ratio} = \text{(scale factor)}^2 \)
\( \text{Volume ratio} = \text{(scale factor)}^3 \)
Congruent = scale factor 1. Scale drawings use ratios (e.g. 1:100).
Example
Example: Scale factor = 3 → Area ×9, Volume ×27
Practice
Lvl 2
Two similar shapes have side ratio 2:3. What is the ratio of their areas?
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