Triangles Classification Worksheet

Lesson Overview

About this worksheet

Every triangle gets TWO names: one for its SIDES and one for its ANGLES. The side classification compares the three side lengths to each other – all equal is equilateral, exactly two equal is isosceles, no two equal is scalene. The angle classification compares each angle to 90 degrees – all three under 90 is acute, exactly one equal to 90 is right, exactly one over 90 is obtuse. Because the three angles always sum to 180, a triangle can have AT MOST one right or obtuse angle.

The reference box at the top of page 1 teaches the two-axis process with a (5, 5, 5) equilateral triangle as the worked example, plus the explicit fact that EVERY equilateral triangle is also acute (since its three 60-degree angles are all under 90). The (5, 5, 5) measurements do NOT appear in any assessed item, and the (60, 60, 60) angle set does NOT appear in any Section B item.

Section A on page 1 has 8 items that give side lengths (such as 4-4-6 or 12-15-20) and ask students to name the triangle by sides only. The item set covers all three categories with deliberate repetition (isosceles appears at items 1, 5, and 7; scalene at 2, 3, and 6; equilateral at 4 and 8) so students cannot just count by position. Section B on page 2 mirrors the structure on the angle axis with 6 items in a 2-column fill-in-the-blank layout, again covering all three categories.

Section C on page 2 has 3 multi-step word problems with work boxes (1.10in): one asks for BOTH names of a (50, 50, 80) isosceles-acute triangle, one asks for BOTH names of a scalene right triangle, and the third is a reasoning challenge – can a triangle have two right angles? (No – two right angles sum to 180, leaving 0 for the third.) Page 3 is a complete answer key.

How to Use This Lesson

Project the page-1 reference and read both classification axes out loud: by SIDES (equilateral/isosceles/scalene) and by ANGLES (acute/right/obtuse).

Walk through the (5, 5, 5) worked example: all three sides equal (equilateral) and three 60-degree angles (acute), so the complete name is ‘equilateral acute triangle’.

Work Section A item 1 (sides 4, 4, 6) together; ask which sides are equal, and connect to the side-name.

Walk through Section A item 4 (sides 6, 6, 6) to anchor the equilateral case before items 5-8.

Assign the rest of Section A independently or with a partner; remind students that they only look at side LENGTHS in Section A (not angles).

Read Section B item 9 (angles 50, 60, 70) together; confirm the sum is 180 and all three are less than 90.

Use Section C item 17 (can a triangle have two right angles?) as a closing discussion about the 180-degree rule.

Use the answer key on page 3 for self-check or aide spot-check.

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