Geometry & measures · Congruence & similarity
Chapter 1 · 4
The idea
Similar shapes & missing lengths
Why equal angles force sides into a fixed ratio, finding the scale factor the right way round, similar triangles hidden inside one figure, and the area and volume scale factors k² and k³.
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Geometry & measures · Congruence & similarity
Similar shapes & missing lengths
Why equal angles force sides into a fixed ratio, finding the scale factor the right way round, similar triangles hidden inside one figure, and the area and volume scale factors k² and k³.
Why it works
Same shape, different size
Similar means same shape, different size. Corresponding angles are equal and corresponding sides are all in the same ratio — that ratio is the scale factor . For triangles, equal angles are enough: if two triangles have the same three angles, their sides must be in proportion.The scale factor: new over old
Pick a pair of corresponding sides where you know both lengths and divide the one in the shape you're going to by the one you're coming from:Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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