geometry · Year 6 · Suggested learning sequence

The quadrilateral family tree

Quadrilaterals belong to families, and one shape can belong to several. A rectangle is any quadrilateral with 4 right angles, so every square is a rectangle. A rhombus is any quadrilateral with 4 equal sides, so every square is a rhombus too. Rectangles and rhombuses are both parallelograms. To test 'Is every A a B?', write down what a B needs, then ask whether every A always has it. Careful: the reverse is often false. Every square is a rectangle, but a long thin rectangle is not a square. Some facts force others: a parallelogram with one right angle has four.

Sample questions

This shape is a parallelogram. A rhombus is a quadrilateral with four equal sides. Is every parallelogram a rhombus?

  1. A rhombus is a quadrilateral with four equal sides.
  2. A parallelogram can have two long sides and two short sides.
  3. So the answer is no.

Answer: no

This shape is a parallelogram. A rectangle is a quadrilateral with four right angles. Is every parallelogram a rectangle?

  1. A rectangle is a quadrilateral with four right angles.
  2. A parallelogram can lean over, so its corners need not be right angles.
  3. So the answer is no.

Answer: no

This shape is a parallelogram. A square is a quadrilateral with four equal sides and four right angles. Is every parallelogram a square?

  1. A square is a quadrilateral with four equal sides and four right angles.
  2. A parallelogram need not have equal sides or right angles.
  3. So the answer is no.

Answer: no

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