Shapes are similar when one is an enlargement of the other: the angles are equal and every length is multiplied by the same scale factor. When DE is parallel to BC in triangle ABC, triangles ADE and ABC are similar.
Find the scale factor from a pair of matching sides, then multiply or divide. If AD = 2 cm and AB = 8 cm, the scale factor from ADE to ABC is 4, so if DE = 3 cm then BC = 12 cm. Be careful to compare matching sides, not sides that happen to be in the same place.
Worked example
AD = 4 cm, DB = 12 cm and DE = 5 cm, with DE parallel to BC. Find BC.
- AB = 4 + 12 = 16, so the scale factor is 16 ÷ 4 = 4.
- BC = 5 × 4 = 20.
Answer:20 cm
Key words
- similar
- same shape, different size
- scale factor
- the multiplier between matching lengths
- corresponding sides
- sides in matching positions
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Common Core-referenced: HSG-SRT.B.5