A scale factor relates corresponding linear lengths in similar figures: a factor greater than 1 enlarges a figure, while a positive factor less than 1 reduces it. Given corresponding lengths and a scale factor, the missing length is found by multiplying or dividing proportionally, using fractions, decimals, ratios, diagrams, or equations; the correspondence of sides must be established rather than assuming an additive change. This scope concerns linear lengths, not the distinct area and volume scale factors introduced in more advanced work.
In similar figures, corresponding sides are multiplied by the same scale factor. First identify which sides correspond, then use multiplication or division.
Example: Triangle is similar to triangle . A side of triangle measures cm, and its corresponding side in triangle measures cm. Another side of triangle measures cm. Find the corresponding side in triangle .
First find the scale factor from triangle to triangle :
So every corresponding length is multiplied by . Let be the missing length:
Therefore, the missing corresponding side measures
You can check the correspondence by comparing ratios:
The lengths change proportionally; they do not increase by the same additive amount.
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