Similarity (Copy)

Lengths in Similar Shapes Cheat Sheet (IGCSE Mathematics 0580 – CORE)
Topic: Calculating Lengths in Similar Shapes

1. Key Concept: Similar Shapes

• Similar shapes have the same shape but different sizes.
• Corresponding sides are proportional (same ratio).
• Corresponding angles are equal.

2. Side Length Ratios

If two shapes are similar, then:

Side length of smaller shapeSide length of larger shape=constant ratio (scale factor)frac{text{Side length of smaller shape}}{text{Side length of larger shape}} = text{constant ratio (scale factor)}

or:

Side length of larger shape=Side length of smaller shape×scale factortext{Side length of larger shape} = text{Side length of smaller shape} times text{scale factor}

3. How to Find Missing Lengths

Steps:

1. Identify corresponding sides.
2. Find the scale factor:
   • Scale factor = larger side ÷ smaller side
   • or given directly in the question.
3. Multiply or divide to find missing side:
   • Multiply by scale factor to get a larger side.
   • Divide by scale factor to get a smaller side.

4. Important Formulas

5. Examples

• Example 1:
  Two similar triangles. One side of the small triangle is 5 cm.
  Scale factor = 3.
  Larger triangle side = 5 × 3 = 15 cm.
• Example 2:
  Two similar rectangles. One side of the large rectangle is 18 cm.
  Scale factor = 2.
  Smaller rectangle side = 18 ÷ 2 = 9 cm.

6. Tips

• Always check whether you are moving from smaller to larger shape (multiply) or larger to smaller shape (divide).
• Make sure you match corresponding sides correctly.
• Scale factor is always positive and describes enlargement or reduction.

This covers CORE-level calculation methods for finding missing lengths in similar shapes — no area or volume scaling required.