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Unit 12 · ShapePearson Edexcel IGCSE · 4MA1 Higher

Similarity, Congruence & Scale Factors

Similar shapes, area and volume scale factors. Congruence conditions (SSS, SAS, ASA, RHS). Grade 6–8 topic.

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Corbett MathsSimilar shapes — area and volume scale factors
GCSE Maths TutorSimilar Shapes - Area and Volume Scale Factors | GCSE Maths Tutor
Key facts & methods

Similar shapes — fill in the table

TermRule
Similar shapes
Linear scale factor (LSF)
Area scale factor (ASF)
Volume scale factor (VSF)
Scale drawings (e.g. 1:50,000)

Congruence conditions — fill in the table

ConditionWhat it means
Congruent
SSS
SAS
ASA
RHS
AAS
SSA
Exam questions — 4 questions · 9 marks · Edexcel 4MA1 style
⚡ Show ALL working — the AI awards method marks just like a real examiner. Partial credit for correct working even if the final answer is wrong.
3 marksSimilar shapes — find length4MA1 style 🔢 Calculator

Two similar triangles have corresponding sides of 6 cm and 10 cm. The area of the smaller triangle is 27 cm². Find the area of the larger triangle. (3 marks)

Hint: Linear scale factor = ratio of corresponding lengths. Area scale factor = (LSF)². Multiply the known area by the ASF.
+30 XP
3 marksVolume scale factor4MA1 style 🔢 Calculator

Two similar cones have radii 4 cm and 6 cm. The volume of the smaller cone is 64π cm³. Find the volume of the larger cone. (3 marks)

Hint: LSF = ratio of radii = 6/4. VSF = (LSF)³. Multiply the known volume by VSF.
+30 XP
1 markCongruence condition4MA1 style

Two triangles have sides 5cm, 7cm, 9cm and 5cm, 7cm, 9cm respectively. What congruence condition applies?

A SAS
B ASA
C SSS
D RHS
1 markArea from scale factor4MA1 style

Two similar rectangles have lengths in ratio 2:5. If the smaller has area 16 cm², what is the larger area?

A 40 cm²
B 100 cm²
C 200 cm²
D 64 cm²
Quick recall flashcards

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