Maths›Similarity, Congruence & Scale Factors
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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
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Key facts & methods

Similar shapes

  • Two shapes are similar if corresponding angles are equal and corresponding sides are in the same ratio.
  • Linear scale factor (LSF) = ratio of corresponding lengths. E.g. if sides are in ratio 3:5, LSF = 5/3.
  • Area scale factor (ASF) = LSF². E.g. if LSF = 3, ASF = 9. Areas are 9 times bigger.
  • Volume scale factor (VSF) = LSF³. E.g. if LSF = 2, VSF = 8.
  • Maps and scale drawings: a scale of 1:50,000 means 1 cm on map = 50,000 cm = 500 m in real life.

Congruence conditions

  • Two triangles are congruent if they are identical in shape and size.
  • SSS — three sides equal.
  • SAS — two sides and the included angle equal.
  • ASA — two angles and a side equal.
  • RHS — right angle, hypotenuse and one other side equal.
  • AAS also works (two angles and a non-included side).
  • Note: SSA does NOT prove congruence (ambiguous case).
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

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