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2D Shape Properties

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2D Shape Properties

Use the shape descriptions in the next section to investigate quadrilaterals. Remember: a regular polygon has all sides equal and all interior angles equal. In New Zealand, a trapezium has at least one pair of parallel sides.

Read the shapes

Use these descriptions for Questions 1–3. Shape A is a square. Shape B is a rectangle that is not a square. Shape C is a rhombus that is not a square. Shape D is a parallelogram that is neither a rectangle nor a rhombus. Each shape has two pairs of parallel opposite sides.

1.Which labelled shape is both a rectangle and a rhombus? Explain which two properties make it both.
2.Select every shape in the descriptions that has two pairs of parallel opposite sides.
  • A only
  • A and B only
  • A, B, C and D
  • C and D only
3.Shape D is a parallelogram but not a rectangle. State one property it shares with a rectangle and one property it does not have.

Classify and reason

Use precise geometry vocabulary in your explanations.

4.A polygon has five sides and five vertices. Complete the description: it is a .
5.A polygon has five equal sides and five equal interior angles. Complete the description: it is a polygon.
6.Match each triangle classification to its defining side property.
  • Equilateral
  • Isosceles
  • Scalene
  • At least two sides equal
  • All three sides equal
  • All three sides different
7.True or false: Every square is a rectangle, but not every rectangle is a square. Give a reason for your choice.
TrueFalse
8.A quadrilateral has exactly one pair of parallel sides. Using the New Zealand definition given above, what is it called? Could it also be a parallelogram? Explain.
9.A triangle has angles of 48° and 67°. Calculate its third angle, then classify the triangle by its angles.

Design challenge

Think about the conditions before you draw. Your answer should be possible to check from the diagram.

10.Draw a quadrilateral with exactly two right angles and no parallel sides. Mark the right angles and explain how your drawing meets both conditions.
11.Mere is designing a regular polygon for a repeating pattern. She wants each interior angle to be 120°. How many sides must the polygon have? Show how you know.

2 printable pages

  • 2D Shape Properties, page 1 of 2: Read the shapes, Classify and reason

    Page 1

  • 2D Shape Properties, page 2 of 2: Design challenge

    Page 2

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