Study guides › Level 7 · Geometry

Similar triangles

Level 7 · Geometry · for questions like “Triangle ABC is similar to triangle DEF. AB = 4, BC = 6 and DE = 10. How long is EF?”

💡 The idea

Similar shapes are the same shape at a different size. Every side is scaled by the same factor.

🪜 The steps

1. Match the sides: AB ↔ DE, BC ↔ EF, CA ↔ FD (the letters in the same order).
2. Find the scale factor: DE ÷ AB.
3. Multiply the matching side by it.

✏️ Worked examples

1. AB = 4, DE = 10: the factor is 10 ÷ 4 = 2.5. EF = 6 × 2.5 = 15.

2. AB = 9, DE = 6, BC = 12: the factor is 6/9 = 2/3. EF = 12 × 2/3 = 8.

⚠️ Watch out

• The factor can be smaller than 1 when the second triangle is smaller.
• Match the sides by the order of the letters, not by where they sit on the page.

🎯 Try these

1. AB = 3, DE = 12, BC = 5. EF?
2. AB = 10, DE = 4, BC = 15. EF?
3. AB = 6, DE = 9, BC = 8. EF?

Answers: 1) 20 2) 6 3) 12

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.