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Grade 8–9 · Geometry of 2D Shapes
Construction of Geometric Figures
MEMORANDUM
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Class: 
Date: 
Mark
  / 13

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 two instruments may you use in a construction?
    (1)
    A compass and a ruler (straight edge) only.✓ (1)
  2. 2
    Why must you not rub out your arcs?
    (1)
    The arcs are the working — the marks are awarded for them.✓ (1)
  3. 3
    When bisecting AB, how wide must the compass be opened?
    (2)
    More than half of AB, or the arcs will not cross.✓✓ (2)
  4. 4
    What angle does a perpendicular bisector make with the line?
    (1)
    90°✓ (1)
  5. 5
    How do you construct a 30° angle?
    (2)
    Construct 60°, then bisect it.✓✓ (2)
  6. 6
    How do you construct a 45° angle?
    (2)
    Construct 90°, then bisect it.✓✓ (2)
  7. 7
    Which side is usually the most convenient to draw first in an SSS construction?
    (1)
    Usually the longest side, because it gives a clear base — but any of the given sides can be used.✓ (1)
  8. 8
    Can a triangle with sides 3 cm, 4 cm and 9 cm be constructed?
    (2)
    2 cm9 cm3 cm4 cmthe two arcs fall short of each other
    No — 3 + 4 = 7, which is less than 9, so the arcs never meet.✓✓ (2)
  9. 9
    Each angle of a constructed equilateral triangle measures…
    (1)
    6 cm6 cm6 cmarcs of the same radius from both ends
    60°✓ (1)
TOTAL: 13 marks
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