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Year 8 Maths — Quadrilaterals

Use the properties of a parallelogram and the mid-point theorem.

Name: ________________________

Before you start

A parallelogram with one diagonal drawn across it. Find the two pieces the diagonal makes, and the diagonal itself.

123
  1. 1. One of the two triangles
  2. 2. The other triangle — the same size and shape, turned round
  3. 3. The diagonal that makes them

Turn either triangle half a turn about the middle of the diagonal and it lands exactly on the other one. Opposite sides equal and opposite angles equal both fall straight out of that single fact.

  1. 1.One side of a parallelogram is 8 cm long. How long is the side opposite it, in centimetres?

  2. 2.In triangle PQR, the segment joining the mid-points of PQ and PR is 9 cm long. How long is QR, in centimetres?

  3. 3.Match each quadrilateral to the property that sets it apart.

    • Parallelogram
    • Rectangle
    • Rhombus
    • Square
    • Kite
    • All four angles are right angles
    • All four sides are equal
    • Both pairs of opposite sides are parallel
    • Two pairs of equal sides, next to each other rather than opposite
    • All four sides equal and all four angles right angles

  4. 4.In triangle ABC, D is the mid-point of AB and E is the mid-point of AC. BC is 12 cm long. How long is DE, in centimetres?

  5. 5.Sort each property by whether every parallelogram has it.

    Groups: Every parallelogram · Not every parallelogram

    • The diagonals are equal in length
    • Every angle is a right angle
    • The diagonals cut each other in half
    • Opposite sides are equal
    • Opposite angles are equal
    • All four sides are equal

  6. 6.Which of these is true of every rhombus but not of every parallelogram?

    • a) Opposite angles are equal
    • b) Opposite sides are parallel
    • c) The diagonals cut each other in half
    • d) All four sides are equal

  7. 7.The mid-point theorem says the segment joining the mid-points of two sides of a triangle is...

    • a) twice the length of the third side
    • b) perpendicular to the third side
    • c) equal in length to the third side
    • d) parallel to the third side and half its length

  8. 8.One angle of a parallelogram is 65°. How big is the angle opposite it, in degrees?

Answer key — Year 8 Maths — Quadrilaterals

  1. 1. 8
  2. 2. 18
  3. 3. Parallelogram → Both pairs of opposite sides are parallel; Rectangle → All four angles are right angles; Rhombus → All four sides are equal; Square → All four sides equal and all four angles right angles; Kite → Two pairs of equal sides, next to each other rather than opposite
  4. 4. 6
  5. 5. Opposite sides are equal → Every parallelogram; Opposite angles are equal → Every parallelogram; The diagonals cut each other in half → Every parallelogram; All four sides are equal → Not every parallelogram; The diagonals are equal in length → Not every parallelogram; Every angle is a right angle → Not every parallelogram
  6. 6. d) All four sides are equal
  7. 7. d) parallel to the third side and half its length
  8. 8. 65