Three Sides, Three Angles: Classifying Triangles

About This Resource

A free Grade 5 math worksheet on classifying triangles in two ways: by their sides (equilateral, isosceles and scalene) and by their largest angle (acute, right and obtuse). Students sort triangles from their side lengths and angle sizes, decide which combinations are possible, such as a right isosceles triangle, and explain their thinking. Includes a timed lesson plan, a six-activity worksheet, an editable Word version and answer key.

Overview

Students learn that every triangle can be named in two ways. By its sides: an equilateral triangle has three equal sides, an isosceles triangle has two equal sides and a scalene triangle has no equal sides. By its angles: an acute triangle has three angles less than 90°, a right triangle has one 90° angle and an obtuse triangle has one angle more than 90°. Students classify triangles from side lengths and angle sizes, and reason about which combinations can and cannot exist.

Resource Details

Subject: Math
Topic: Classifying Triangles
Category: Shapes & Geometry
File Type: PDF
File Size: 237.5 KB
Published: 08 Nov 2026
Downloads: 0

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Grade 5 math (ages 10–11) 45 minutes Geometry properties of shapes classifying reasoning vocabulary

Student Task

Draw three triangles on the board and ask: "How are they different?" Collect ideas about sides and corners.
Do activities 1 and 2 together, measuring or comparing sides and angles.
Students complete activities 3 to 6 on their own. Answers are in the answer key.

Classroom Use

Straw triangles: students make triangles from straws of different lengths and name each one by its sides.
Corner test: hold the corner of a sheet of paper against each angle of a triangle to see if it is smaller than, equal to or bigger than a right angle.
Two-name challenge: students try to draw a triangle for every pair of names, such as right scalene or obtuse isosceles.

Differentiation

Support: give students a reference card with a picture of each type of triangle. Challenge: students explain why an equilateral triangle can never be right or obtuse.

Answer Key & Assessment

Activities 1 to 5 check classifying triangles by sides and angles (answer key included). Activity 6 shows whether students can reason about which combinations are possible.

Learning Objectives

Classify triangles by their sides as equilateral, isosceles or scalene.
Classify triangles by their angles as acute, right or obtuse.
Explain which combinations of side and angle types are possible.

Teacher Tips

Remind students that a triangle can have at most one right angle or one obtuse angle, because the three angles always add up to 180°. A square corner of paper is a quick way to check for right angles.

What's Included

6-page printable PDF lesson pack: teacher lesson plan with timings, materials and differentiation
Key vocabulary list (6 words with meanings and examples)
Student worksheet (6 activities)
Editable Word version of the worksheet
Complete answer key (also as a separate PDF)