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Grade 8 · Geometry of 2D Shapes
Congruent & Similar 2D Shapes
MEMORANDUM
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  / 16

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    What does it mean if two shapes are congruent?
    (2)
    Same shape and same size — identical.✓✓ (2)
  2. 2
    What does it mean if two shapes are similar?
    (2)
    Same shape, different size: equal angles and sides in proportion.✓✓ (2)
  3. 3
    Are all congruent shapes also similar?
    (2)
    Yes — with a scale factor of 1.✓✓ (2)
  4. 4
    Are all similar shapes congruent?
    (2)
    No — only when the scale factor is 1.✓✓ (2)
  5. 5
    Two similar triangles: sides 5 cm and 8 cm; the matching side to 5 is 15 cm. Find the other.
    (2)
    5815?drawn at the same scale
    Scale factor 3 → 8 × 3 = 24 cm✓✓ (2)
  6. 6
    A rectangle 4 cm × 6 cm is enlarged by scale factor 2. What are the new sides?
    (2)
    8 cm × 12 cm✓✓ (2)
  7. 7
    Triangle A: 3, 5. Triangle B: 9, 15. Similar?
    (2)
    35915drawn at the same scale
    9÷3 = 3 and 15÷5 = 3 → Yes, scale factor 3.✓✓ (2)
  8. 8
    Triangle A: 2, 4. Triangle B: 6, 10. Similar?
    (2)
    24612drawn at the same scale
    6÷2 = 3 but 10÷4 = 2,5 → No, ratios differ.✓✓ (2)
TOTAL: 16 marks
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