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Grade 10 · Euclidean Geometry
The Midpoint Theorem (Grade 10)
MEMORANDUM
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Mark
  / 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
    State the midpoint theorem.
    (2)
    The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.✓✓ (2)
  2. 2
    D and E are midpoints of AB and AC; BC = 14 cm. Find DE.
    (2)
    7 cm✓✓ (2)
  3. 3
    D and E are midpoints of AB and AC; BC = 25 cm. Find DE.
    (2)
    12,5 cm✓✓ (2)
  4. 4
    D and E are midpoints; DE = 6,5 cm. Find BC.
    (2)
    13 cm✓✓ (2)
  5. 5
    D and E are midpoints; DE = 9 cm. Find BC.
    (2)
    18 cm✓✓ (2)
  6. 6
    State the converse of the midpoint theorem.
    (2)
    A line through the midpoint of one side, parallel to a second side, bisects the third side.✓✓ (2)
  7. 7
    D is the midpoint of AB and DE ∥ BC. What can you conclude about E?
    (2)
    E is the midpoint of AC (converse of the midpoint theorem).✓✓ (2)
  8. 8
    Why are △ADE and △ABC similar?
    (2)
    They share ∠A and AD:AB = AE:AC = 1:2.✓✓ (2)
TOTAL: 16 marks
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