Teaching Math: Classifying Triangles by Sides and Angles

Students in intermediate and middle school must learn to classify triangles. Triangles are the simplest polygons, having 3 sides and 3 angles. The measures of the interior angles of any triangle add up to 180°. There are two ways students in this age group learn to name triangles: by their sides and by their angles. As an upper elementary and middle-school math teacher, I found I really needed to emphasize these two distinctions. Hands-on experiences always work best at the onset.

Prerequisites

First of all, students need to understand angle types and how to measure angles. Click here for memory tricks and hands-on activities for classifying and naming angles. They also need to know that congruent means having the same measure or length.

Introduce Vocabulary, and Show Pictures of Each Type of Triangle.

As you discuss vocabulary with the students, use this program by Learning Wave to show students what each triangle type looks like. They should create matching sketches in their math notes.

Vocabulary for Classifying Triangles by Their Sides

Equilateral triangle: 3 congruent sides
Isosceles triangle: 2 congruent sides (at least)
Scalene triangle: 0 congruent sides
Note: mention that sides marked with the same number of slashes are congruent.

Hands-on Practice Classifying Triangles by Sides

Materials: straws, scissors, rulers, tape, marker, tag board, math notes on classifying triangles
Place students into pairs or small groups. Each group creates one equilateral triangle, one isosceles and one scalene triangle from the straws. They tape them onto tag board and label each triangle according to sides. Display them in class.

Vocabulary for Classifying Triangles by Their Angles

Acute triangle: All angles measure less than 90°
Equiangular triangle: All angles measure exactly 60° (equal angles)
Obtuse triangle: one angle measures over 90°
Right triangle: one angles measures exactly 90°

Hands-on Practice Classifying Triangles by Angles

Materials: straws, scissors, tape, rulers, marker, tag board, protractors, math notes on classifying triangles
Place students into pairs or small groups. Each group creates one acute triangle, one equiangular triangle, one obtuse triangle, and one right triangle from the straws. They should double-check the measures of the angles, and all group members must agree with the classifications. They tape the creations onto tag board and label each triangle according to angles. Display them in class.

Overlapping Classifications

Point out that the categories can overlap. Words like "is always" or "may be" could apply. For example, a right triangle may be scalene or isosceles, but it's never equilateral, acute or obtuse.

Practice Worksheets and Review Videos

Computer Review of Triangle Classifications: Use this practice from Study Zone on your computer as a review with the entire class before they are placed into hands-on groups.

Explanation Video: If a student is absent for the lesson on classifying triangles, he can view this video explaining how to classify triangles. The lesson is less than 5 minutes. (Please note: the guy in the video spells isosceles incorrectly.)

Sketchpad: If you use Sketchpad, the Learning Center has activities designed for using Sketchpad's tools to construct triangles.

Interactive Game: Crickweb has an online interactive practice called "Shapes" where students 'grab' the triangles and drag them into the equilateral, isosceles, or scalene groups. Simple quadrilateral shapes are also included.

Printable Practice Sheet: In this printable worksheet from Kuta Software, students are asked to classify 12 triangles according to sides and angles.

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