Similarity and congruence
Cambridge IGCSE Mathematics (0580) · Unit 4: Geometry · 9 flashcards
Similarity and congruence is topic 4.8 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 4 — Geometry , alongside Angles, Angles in polygons and Parallel lines. In one line: Shapes are similar if they have the same angles and their corresponding sides are in proportion (equal ratios). One shape is an enlargement or reduction of the other, maintaining the same overall form.
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.
The deck below contains 9 flashcards — 3 definitions and 1 key concept — covering the precise wording mark schemes reward. Use the 3 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
'similar' in the context of geometric shapes
Shapes are similar if they have the same angles and their corresponding sides are in proportion (equal ratios). One shape is an enlargement or reduction of the other, maintaining the same overall form.
Questions this Similarity and congruence deck will help you answer
- › Explain the difference between similarity and congruence.
Define 'similar' in the context of geometric shapes.
Shapes are similar if they have the same angles and their corresponding sides are in proportion (equal ratios). One shape is an enlargement or reduction of the other, maintaining the same overall form.
What does it mean for two triangles to be 'congruent'?
Two triangles are congruent if they are exactly the same. This means all corresponding sides and angles are equal. There are four congruence tests: SSS, SAS, ASA, RHS.
Triangle ABC has sides 3cm, 4cm, and 5cm. Triangle XYZ has sides 6cm, 8cm, and 10cm. Are they similar? Explain.
Yes, they are similar. The sides are in the ratio 3:6, 4:8, and 5:10, which simplifies to 1:2. Since all corresponding sides are in the same ratio, the triangles are similar.
State the condition for Side-Angle-Side (SAS) congruence.
Two triangles are congruent by SAS if two sides and the included angle (the angle between those two sides) of one triangle are equal to the corresponding two sides and included angle of the other triangle.
A rectangle has sides of length 2 and 5. A similar rectangle has a corresponding side of length 10. What is the length of the other side of the larger rectangle?
The scale factor is 10/2 = 5. Therefore, the other side length is 5 * 5 = 25.
The area scale factor between two similar figures is 9. What is the length scale factor?
The area scale factor is the square of the length scale factor. Therefore, the length scale factor is the square root of 9, which is 3.
The volume scale factor between two similar solids is 8. What is the length scale factor?
The volume scale factor is the cube of the length scale factor. Therefore, the length scale factor is the cube root of 8, which is 2.
Shapes A and B are similar. The ratio of their corresponding sides is 3:4. If the area of Shape A is 45 cm², what is the area of Shape B?
The area scale factor is (4/3)² = 16/9. Area of Shape B = (16/9) * 45 cm² = 80 cm².
Explain the difference between similarity and congruence.
Similar shapes have the same angles and proportional sides (equal ratios), so one is an enlargement of the other. Congruent shapes are exactly identical; they have the same angles and the same side lengths.
Key Questions: Similarity and congruence
Define 'similar' in the context of geometric shapes.
Shapes are similar if they have the same angles and their corresponding sides are in proportion (equal ratios). One shape is an enlargement or reduction of the other, maintaining the same overall form.
What does it mean for two triangles to be 'congruent'?
Two triangles are congruent if they are exactly the same. This means all corresponding sides and angles are equal. There are four congruence tests: SSS, SAS, ASA, RHS.
State the condition for Side-Angle-Side (SAS) congruence.
Two triangles are congruent by SAS if two sides and the included angle (the angle between those two sides) of one triangle are equal to the corresponding two sides and included angle of the other triangle.
More topics in Unit 4 — Geometry
Similarity and congruence sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Similarity and congruence deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
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