Edexcel IGCSE Maths 复习笔记 4.17.1 Similarity - Lengths

Edexcel IGCSE Maths 复习笔记 4.17.1 Similarity - Lengths

What are similar shapes?

  • Two shapes are mathematically similar if one is an enlargement of the other
  • Equivalent angles in the two shapes will be equal
  • Equivalent lengths in the two shapes will be in the same ratio and are linked by a scale factor (which you will normally have to find)

Working with similar shapes

  1. Identify equivalent known lengths
  2. Establish direction (getting bigger or smaller?)
  3. Find scale factor = Second Length ÷ First Length(Check that SF > 1 if getting bigger and SF < 1 if getting smaller)
  4. Use scale factor to find length

Exam Tip

If similar shapes overlap on the diagram (or are not clear) draw them separately!For example, in this diagram the triangles ABC and APQ are similar:So we would redraw them separately before we start:Similar-Triangles-togetherSimilar-Triangles-separately

Worked Example