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Grade 10 · Euclidean Geometry
Properties of Quadrilaterals & Their Proofs (Grade 10)
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Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    Two co-interior angles of a parallelogram are (3x + 10)° and (x + 30)°. Determine the value of x, and hence the size of each angle.
    (4)
  2. 2
    Define a parallelogram.
    (2)
  3. 3
    Which quadrilateral has diagonals that are equal AND bisect each other?
    (1)
  4. 4
    Which quadrilateral has perpendicular diagonals that bisect the angles?
    (1)
  5. 5
    How many pairs of parallel sides does a trapezium have?
    (1)
  6. 6
    Do a kite's diagonals bisect each other?
    (1)
  7. 7
    In parallelogram ABCD, Â = 70°. Find Ĉ and B̂.
    (2)
    A70°B?CD
  8. 8
    State five ways to prove a quadrilateral is a parallelogram.
    (4)
  9. 9
    Is every rectangle a parallelogram? Is every parallelogram a rectangle?
    (2)
TOTAL: 18 marks
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