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Year 7 Quadrilaterals Worksheet

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Year 7 Quadrilaterals Worksheet

A community team is designing a small outdoor pavilion using quadrilateral floor tiles. Solve the geometry clues to help them choose and label the shapes. Show working for calculations. Use the UK definition: a trapezium has exactly one pair of parallel sides.

Shape clues

Use the quadrilateral property cards below, then answer Questions 1–5.

RECTANGLE Opposite sides parallel and equal; four right angles.

PARALLELOGRAM Opposite sides parallel and equal; opposite angles equal.

RHOMBUS Four equal sides; opposite sides parallel; diagonals meet at right angles.

TRAPEZIUM Exactly one pair of parallel sides.

1.Which shape is not a quadrilateral: kite, rectangle, triangle or trapezium?
  • Kite
  • Rectangle
  • Triangle
  • Trapezium
2.A tile has two pairs of parallel sides and four right angles. What is its most specific name?
3.Select every property that always applies to a rhombus.
  • All four sides are equal
  • All four angles are right angles
  • Both pairs of opposite sides are parallel
  • Its diagonals bisect each other at right angles
4.The team makes a parallelogram tile with one angle of 68°. Find its other three interior angles.
5.A four-sided tile has interior angles 82°, 97° and 104°, plus one unknown angle. What is the unknown angle?

Work out the design

Use the properties and angle facts to solve the pavilion design problems.

6.A rhombus-shaped border has a perimeter of 36 cm. What is the length of each side? Show the division you use.
7.A trapezium tile has a pair of parallel sides. One of the two angles along the same sloping side is 71°. The other is x°. Find x and explain the angle fact used.
8.True or false? Every square is a rectangle, but not every rectangle is a square. Explain briefly.
9.Match each description to its most specific quadrilateral: (a) four equal sides and four right angles; (b) exactly one pair of parallel sides; (c) two pairs of parallel sides, but no right angles and not all sides equal.
  • (a) Four equal sides and four right angles
  • (b) Exactly one pair of parallel sides
  • (c) Two pairs of parallel sides, no right angles and not all sides equal
  • Trapezium
  • Parallelogram
  • Square
10.A designer says, “Opposite angles in every parallelogram are equal, so all four angles must be equal.” Is the conclusion correct? Use a non-rectangular example or angle values to support your answer.
11.Sketch and label a trapezium with exactly one pair of parallel sides and two right angles. Mark the parallel sides with matching arrows and mark the right angles. What is a usual name for this type of trapezium?

3 printable pages

  • Year 7 Quadrilaterals Worksheet, page 1 of 3: Shape clues

    Page 1

  • Year 7 Quadrilaterals Worksheet, page 2 of 3: Work out the design

    Page 2

  • Year 7 Quadrilaterals Worksheet, page 3 of 3: 11. Sketch and label a trapezium with exactly one pair of parallel sides and two right…

    Page 3

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