Triangles and Quadrilaterals
Lessons in this chapter
About Triangles and Quadrilaterals
Geometry in 5th grade is about classification, and it ends with something genuinely new: a hierarchy, where categories contain one another.
Classify Triangles Based on Their Angles and Classify Triangles Based on Their Sides keep the two schemes separate before combining them. Acute, right and obtuse describe the angles; equilateral, isosceles and scalene describe the sides, and every triangle has one label from each list.
Classify Quadrilaterals Based on Their Properties returns to the four-sided family with the full set of tests: parallel sides, equal sides, right angles, equal diagonals.
Classify Quadrilaterals in a Hierarchy Based on Properties is the important lesson. The categories nest: every square is a rhombus and a rectangle, every rhombus and rectangle is a parallelogram, every parallelogram is a quadrilateral. Each step down adds a condition rather than replacing one.
That nesting is a child's first encounter with a classification where one object belongs to several categories at once, and it is the structure that definitions in later geometry rely on.
All four lessons open as a 5th grade math worksheet in the page. Classify Triangles Based on Their Angles, Classify Quadrilaterals Based on Their Properties and Classify Quadrilaterals in a Hierarchy Based on Properties each set their own questions, scored as you answer them. They are free to try, with no login needed for your first 3.
Frequently asked questions
Classify Triangles Based on Their Angles and Classify Triangles Based on Their Sides keep the two schemes separate before combining them, so every triangle carries one label from each list. Classify Quadrilaterals Based on Their Properties returns to the four-sided family with the full set of tests, and Classify Quadrilaterals in a Hierarchy Based on Properties is the important lesson, where the categories nest and every square is also a rhombus, a rectangle and a parallelogram. The chapter sits in the Common Core domain Geometry (5.G).
Two ways at once. By angles as acute, right or obtuse, and by sides as equilateral, isosceles or scalene. Every triangle gets one label from each scheme.
A nesting of categories. Every square is a rhombus and a rectangle, every rhombus and rectangle is a parallelogram, and every parallelogram is a quadrilateral.
Because each category is defined by conditions, and a shape belongs to every category whose conditions it meets. A square meets all of them, so it has the most names.
No. An equilateral triangle has three 60 degree angles, so none of them can be 90. It is a good example of how the two classification schemes constrain each other.
A rhombus has four equal sides; a rectangle has four right angles. A square has both, which is why it belongs to each category.