Similar shapes
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Similar shapes
Two shapes are similar when angles match and sides share one scale factor.
Proving two triangles similar
Two matched angles are enough to prove similarity.
Missing lengths in similar shapes
Finding the scale factor from one matched pair of sides.
A proof of Pythagoras’ theorem
Why a² + b² = c², proved with the similar triangles an altitude cuts a.
Areas of similar shapes
A length scale factor k scales every area by k².
Volumes of similar solids
A length scale factor k scales volume by k³.