Grade 4 Geometry: Classifying Shapes

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   A quadrilateral has exactly 1 pair of parallel sides. Those parallel sides are 8 cm and 3 cm long. What is the best name for it: square, rectangle, rhombus, parallelogram, or trapezoid?

   1. Check parallel sides first, then equal sides, then right angles. The best name is the most exact one that fits.
   2. Exactly 1 pair of parallel sides means it is not a parallelogram — so it is not a square, rectangle or rhombus either.
   3. A quadrilateral with exactly 1 pair of parallel sides is a trapezoid.

   Answer: trapezoid

2. Example 2

   A quadrilateral has 4 right angles. Two sides are 9 cm long and the other two sides are 5 cm long. What is the best name for it: square, rectangle, rhombus, parallelogram, or trapezoid?

   1. Check parallel sides first, then equal sides, then right angles. The best name is the most exact one that fits.
   2. It has 4 right angles — which names fit that? Then check the sides: are 9 cm and 5 cm equal?
   3. Its sides are not all equal (9 cm and 5 cm), so it is not a square — it is a rectangle.

   Answer: rectangle

3. Example 3

   A quadrilateral has 4 sides that are each 3 cm long and 4 right angles. What is the best name for it: square, rectangle, rhombus, parallelogram, or trapezoid?

   1. Check parallel sides first, then equal sides, then right angles. The best name is the most exact one that fits.
   2. Check the sides: are they all equal? Check the angles: are they all right angles? Which name needs both?
   3. A rhombus with 4 right angles is a square.

   Answer: square