Similarity Math Example 1

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Example 1

medium
Triangle ABCABC is similar to triangle DEFDEF. If AB=6AB = 6, BC=8BC = 8, AC=10AC = 10, and DE=9DE = 9, find EFEF and DFDF.

Solution

  1. 1
    Find the scale factor: k=DEAB=96=1.5k = \frac{DE}{AB} = \frac{9}{6} = 1.5.
  2. 2
    Multiply each corresponding side by the scale factor: EF=BC×1.5=8×1.5=12EF = BC \times 1.5 = 8 \times 1.5 = 12.
  3. 3
    DF=AC×1.5=10×1.5=15DF = AC \times 1.5 = 10 \times 1.5 = 15.

Answer

EF=12,DF=15EF = 12, \quad DF = 15
Similar figures have equal corresponding angles and proportional corresponding sides. The ratio between any pair of corresponding sides is constant (the scale factor).

About Similarity

Two figures are similar if they have the same shape but possibly different sizes, meaning all corresponding angles are equal and all corresponding sides are in the same ratio (the scale factor).

Learn more about Similarity →

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