Grade 5 Geometry: Shape Hierarchy

Worked examples

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

1. Example 1

   A quadrilateral has exactly one pair of parallel sides. What is its most specific name?

   1. It has 4 straight sides, so it is a quadrilateral.
   2. Only one pair of its sides is parallel. A parallelogram needs 2 pairs, so it is not a parallelogram.
   3. Its most specific name is trapezoid.

   Answer: trapezoid

2. Example 2

   How many of these names are true for EVERY rhombus: polygon, parallelogram, quadrilateral, and rectangle?

   1. Check each name against what EVERY rhombus has.
   2. polygon — yes, it is a closed shape with straight sides; parallelogram — yes, both pairs of its opposite sides are always parallel; quadrilateral — yes, it has 4 sides; rectangle — no: a rectangle needs 4 right angles, and a rhombus doesn't always have that.
   3. So 3 of the names are true for every rhombus.

   Answer: 3

3. Example 3

   A quadrilateral has 4 right angles. Two sides are 6 in long and two sides are 9 in long. What is its most specific name?

   1. It has 4 right angles (square corners), so it is a rectangle.
   2. Its sides are not all the same length (6 in and 9 in), so it is not a square.
   3. Its most specific name is rectangle.

   Answer: rectangle