IGCSE Similarity: Complete Guide for Cambridge IGCSE Mathematics

IGCSE similarity is an essential geometry topic in Cambridge IGCSE Mathematics that appears in both Paper 2 and Paper 4. Mastering similar triangles, similarity ratios, and scale factors is essential for solving geometry problems involving proportional shapes.

This comprehensive IGCSE similarity guide covers everything you need to know, including conditions for similarity, finding missing sides, scale factors, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to identify similar shapes, find missing sides using similarity, calculate scale factors, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Geometry practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Similarity Matters

IGCSE similarity is an essential geometry topic. Here’s why it’s so important:

• High frequency topic: Similarity questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for understanding proportional relationships in geometry
• Exam weight: Typically worth 5-8 marks per paper
• Real-world applications: Used in scaling, maps, and design
• Problem-solving skills: Develops proportional reasoning

Key insight from examiners: Students often confuse similarity with congruence or make errors with scale factors. This guide will help you master these systematically.

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Understanding Similarity

Similar shapes have the same shape but different sizes. Corresponding angles are equal and corresponding sides are in proportion.

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Conditions for Similar Triangles

Triangles are similar if:

1. AAA - All three angles are equal
2. SSS - All three sides are in proportion
3. SAS - Two sides are in proportion and included angle is equal

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Scale Factor

Scale factor = (length in larger shape) / (length in smaller shape)

Example 1: Two similar triangles. In the smaller triangle, a side is 3 cm. In the larger triangle, the corresponding side is 9 cm. Find the scale factor.

Solution: Scale factor = 9 / 3 = 3

Answer: 3

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Finding Missing Sides

Example 2: Triangles ABC and DEF are similar. AB = 4 cm, DE = 6 cm, BC = 5 cm. Find EF.

Solution: Scale factor = 6 / 4 = 1.5 EF = 5 × 1.5 = 7.5 cm

Answer: 7.5 cm

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Area and Volume Scale Factors

Area scale factor = (linear scale factor)² Volume scale factor = (linear scale factor)³

Example 3: Two similar shapes have linear scale factor 2. Find the area scale factor.

Solution: Area scale factor = 2² = 4

Answer: 4

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Common Examiner Traps

• Confusing similarity and congruence - Similar: same shape, different size; Congruent: same shape and size
• Scale factor errors - Check which direction (enlargement or reduction)
• Area/volume errors - Remember to square (area) or cube (volume) the scale factor

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Practice Questions

Question 1

Two similar triangles have scale factor 3. If a side in the smaller triangle is 4 cm, find the corresponding side in the larger triangle.

Solution: Larger side = 4 × 3 = 12 cm

Answer: 12 cm

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Tutopiya Advantage: Personalised IGCSE Similarity Coaching

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📞 Ready to turn shaky similarity skills into exam-ready confidence? Book a free IGCSE maths trial and accelerate your revision plan.

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Frequently Asked Questions About IGCSE Similarity

What are similar shapes?

Similar shapes have the same shape but different sizes. Corresponding angles are equal and sides are in proportion.

What is a scale factor?

Scale factor is the ratio of corresponding lengths in similar shapes.

How do I find missing sides in similar triangles?

Use the scale factor: multiply or divide by the scale factor to find corresponding sides.

What is the relationship between linear, area, and volume scale factors?

Area scale factor = (linear scale factor)² Volume scale factor = (linear scale factor)³

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Pythagoras Theorem: Complete Guide - Master right-angled triangles
• IGCSE Angle Theorems: Complete Guide - Master angle theorems
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Similarity with Tutopiya

Ready to excel in IGCSE similarity? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
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• Flexible scheduling to fit your revision timetable

Book a free IGCSE maths trial lesson and get personalized support to master similarity and achieve your target grade.

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