Similar figures and scale factors

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Learn it Similar figures have the same shape: matching angles are equal and matching sides are in the same ratio (the scale factor k). Areas scale by k², volumes by k³.

Example: A 2 m stick casts a 3 m shadow; a tower casts a 45 m shadow. How tall is the tower?

Similar triangles: height ÷ shadow is the same.
$\frac{2}{3} = \frac{h}{45}$.
$h = 30$ m.

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