This grade 5 classifying shapes lesson explains classifying two-dimensional figures in one printable page, with definitions, a method and a worked example.
Two-dimensional figures are classified by their attributes: sides, parallel lines, and angles. Attributes of a category belong to every shape in its subcategories, so every square is a rectangle, every rectangle is a parallelogram, and every equilateral triangle is isosceles. Name a shape by its most specific category.
Grade 5 Classifying Shapes Lesson: key facts
- Triangles are classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse).
- A parallelogram has both pairs of opposite sides parallel; a trapezoid has at least one pair.
- A rectangle is a parallelogram with four right angles, and a rhombus is a parallelogram with four equal sides.
- A square is both a rectangle and a rhombus, so it has every attribute of both.
- Attributes of a category belong to all shapes in its subcategories.
How do you classify triangles?
Triangles are sorted in two ways. By sides: an equilateral triangle has 3 equal sides, an isosceles triangle has at least 2 equal sides, and a scalene triangle has no equal sides. By angles: an acute triangle has three angles less than \(90^{\circ}\), a right triangle has one angle of exactly \(90^{\circ}\), and an obtuse triangle has one angle greater than \(90^{\circ}\).
A category is a group of shapes that share certain attributes. A subcategory has all of those attributes plus more. Every equilateral triangle is also isosceles, because 3 equal sides include 2 equal sides.
How do you classify quadrilaterals?
A quadrilateral is a closed shape with 4 straight sides. Look at three attributes: pairs of parallel sides, equal sides, and right angles.
| Shape | Defining attributes |
|---|---|
| Trapezoid | At least one pair of parallel sides |
| Parallelogram | Both pairs of opposite sides parallel |
| Rectangle | A parallelogram with 4 right angles |
| Rhombus | A parallelogram with 4 equal sides |
| Square | 4 equal sides and 4 right angles |
How does the hierarchy of two-dimensional figures work?
Read the diagram from top to bottom. Every shape inherits all the attributes of the boxes above it. Opposite sides of a parallelogram are parallel, so rectangles, rhombuses, and squares all have parallel opposite sides. A square sits at the bottom because it is both a rectangle and a rhombus. Because a trapezoid needs only one pair of parallel sides, every parallelogram is also a trapezoid.
How do you name a quadrilateral?
- Count the sides to confirm it is a quadrilateral.
- Count the pairs of parallel sides.
- Check for four equal sides.
- Check for right angles.
- Give the most specific name that fits.
Example. A shape has 4 sides, both pairs of opposite sides parallel, all sides 5 inches long, and no right angles. It is a parallelogram with 4 equal sides, so it is a rhombus. It is not a square, because it has no right angles.
Classifying Two-Dimensional Figures: frequently asked questions
Is a square a rectangle?
Yes. A rectangle is a parallelogram with four right angles, and a square has four right angles. A square is also a rhombus because its four sides are equal.
Is every rectangle a square?
No. A square needs four equal sides. A rectangle that is 6 inches by 2 inches has four right angles but unequal sides, so it is not a square.
What is the difference between a trapezoid and a parallelogram?
A trapezoid has at least one pair of parallel sides. A parallelogram has two pairs of parallel sides, so every parallelogram is also a trapezoid in the Common Core definition.
Can a triangle be both isosceles and right?
Yes. A triangle with a \(90^{\circ}\) angle and two equal sides is both right and isosceles. Sides and angles are two separate ways to classify.
What does most specific name mean?
It is the name lowest on the hierarchy diagram that still fits the shape. A figure with four equal sides and four right angles can be called a rectangle, but square is the most specific name.
How to use this grade 5 classifying shapes lesson
Use this grade 5 classifying shapes lesson before the worksheet, then check what you learned with the quiz.
See every chapter on the Grade 5 math page.
