Fix the mistake: Similarity of Figures ①

Similarity of Figures ① Meaning of Similarity and Scale Factor

The relationship in which one figure exactly overlaps the other when enlarged or reduced is called similarity. It is represented by the symbol ∽.

Scale Factor

The ratio of the lengths of corresponding sides of two similar figures is called the scale factor. When the scale factor is m:n, the ratios of all corresponding side lengths are m:n.

📘 Example ①
Given △ABC ∽ △DEF, AB=6cm, and DE=4cm, find the scale factor. Also find EF when BC=9cm.
Answer:Scale factor AB:DE = 6:4 = 3:2. EF = 9 × (2/3) = 6cm
💡 Key Point
  • Similarity: a relationship in which figures exactly overlap after enlargement or reduction
  • Scale factor: the ratio of corresponding side lengths (constant for all sides)
  • Corresponding angles are equal

Practice Problems

  1. Given △ABC ∽ △PQR, a scale factor of 2:3, and AB=8cm, find PQ.
  2. In two triangles with a scale factor of 3:5, find the perimeter of the larger triangle when the perimeter of the smaller triangle is 18cm.

Answer and Explanation

  1. Answer:12cm. PQ = 8 × (3/2) = 12.
  2. Answer:30cm. 18 × (5/3) = 30.

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