5th Grade Classifying Two-Dimensional Figures Lesson (Free PDF)
Two-dimensional figures are sorted into categories by their properties. Every square is a rectangle, a rhombus, a parallelogram and a quadrilateral, because it has all of their properties. Triangles are named by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). Tree and Venn diagrams show these groups.
Grade 5 · Common Core State Standards: 5.G.B.3, 5.G.B.4
- A quadrilateral has 4 sides; a parallelogram has two pairs of parallel sides.
- A rectangle has 4 right angles; a rhombus has 4 equal sides; a square has both.
- Every square is a rectangle and a rhombus, but not every rectangle is a square.
- Triangles by sides: equilateral, isosceles, scalene.
- Triangles by angles: acute, right, obtuse.
What is a quadrilateral?
A quadrilateral is a closed shape with 4 straight sides and 4 angles. Special quadrilaterals have extra properties. A parallelogram has two pairs of parallel sides. A rectangle is a parallelogram with 4 right angles. A rhombus is a parallelogram with 4 equal sides. A square has 4 equal sides and 4 right angles. In this book, a trapezoid has at least one pair of parallel sides.
How are the quadrilaterals related?
A shape that belongs to a group has every property of that group. Read the tree from the bottom up. A square is a rectangle and a rhombus, so it is also a parallelogram and a quadrilateral. The reverse is not true. A rectangle that is 6 cm by 3 cm is not a square, because its sides are not all equal. When you name a shape, the most specific name tells the most about it.
How does a Venn diagram show the groups?
Each circle holds shapes with one property. The overlap holds shapes with both properties. Squares have 4 equal sides and 4 right angles, so they go in the overlap. A rhombus with slanted sides has only equal sides, so it goes in the left circle alone. A long rectangle has only right angles, so it goes in the right circle alone. A shape with neither property would go outside both circles.
How do you classify triangles?
Name a triangle by its sides and by its angles. By sides: equilateral (3 equal sides), isosceles (at least 2 equal sides) or scalene (no equal sides). By angles: acute (all angles less than 90°), right (one 90° angle) or obtuse (one angle greater than 90°). A triangle always has two names, one for its sides and one for its angles. For example, a triangle with sides 3, 4 and 5 and a right angle is a scalene right triangle.
- Count the sides and check which are equal or parallel.
- Look for right angles.
- Choose the most specific name.
- Check that the shape has every property of its name.
Questions about classifying two-dimensional figures
Is every square a rectangle?
Yes. A rectangle has 4 right angles and opposite sides equal. A square has 4 right angles and all sides equal, so it has every property of a rectangle.
Is every rectangle a square?
No. A rectangle that is 6 cm by 3 cm has right angles, but its sides are not all equal. Only rectangles with 4 equal sides are squares.
What is the difference between a rhombus and a square?
A rhombus has 4 equal sides. A square has 4 equal sides and 4 right angles. So every square is a rhombus, but a rhombus with no right angles is not a square.
What is a trapezoid?
In this book, a trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases.
Can a triangle be both right and isosceles?
Yes. A triangle with a 90° angle and two equal sides is a right isosceles triangle. Sides and angles are two separate ways of naming the same triangle.
All Grade 5 chapters: Grade 5 math.
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