Classify Triangles in a Hierarchy

Students classify triangles by their side lengths (scalene, isosceles, equilateral) and by their angle types (acute, right, obtuse). They organize these classifications into a hierarchy and identify overlapping categories (e.g., an equilateral triangle is also acute).

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Grade 5 · Classifying 2D Figures · question 1 of 3

0 of 20

20 rungs. A star at the top.

Triangle XYZ — choose its most exact name.

scalene triangle

equilateral triangle

isosceles triangle

How it is taught

0:00 of 3:07

Triangles get names from sides and from angles.

One triangle can hold both kinds of names.

Read it: Equilateral triangles are isosceles too

5 triangles. Tick marks show the equal sides, and a square shows a right angle. Triangles 1, 3 and 5 have at least 2 equal sides, so all 3 are isosceles.

Read the tick marks: sides with the same mark are equal.
Find the biggest angle and hold it against a right angle.
Name the triangle twice: once by its equal sides, once by its biggest angle.

Triangle 1 has 3 equal sides, and 3 is at least 2, so it is isosceles too.

A triangle has at most 1 right angle or 1 angle bigger than a right angle, and that one is its biggest.

So every triangle is acute, right or obtuse, and every triangle is scalene or isosceles.

A triangle keeps every name its marks earn: by its sides and by its biggest angle.

Leaving triangle 1 out of the isosceles count because it has 3 equal sides, not 2.

Isosceles means at least 2 equal sides, and 3 equal sides is at least 2. Triangle 1 counts.

6 triangles: 1 equilateral, 3 with exactly 2 equal sides and 2 with no equal sides. How many are isosceles? — 4. The 3 with 2 equal sides are isosceles, and the equilateral one has 3 equal sides, so it is isosceles too: 4.

A triangle with three 5-inch sides and three 60° angles

Triangles can be sorted two different ways — by their sides, and by their angles.

Here's a triangle. Let's give it the right names!

Grade 5 · Sorting triangles by sides AND angles

First, the sides. This side is five inches long.

This side is also five.

And this one is five too! All three sides are equal.

When all three sides match, we call the triangle equilateral.

Now let's check the angles inside the triangle.

Each angle measures sixty degrees.

Any angle less than ninety degrees is acute. All three are acute!

So this one triangle is both equilateral AND acute. It gets two labels!

That's the hierarchy: every equilateral triangle is also acute.

Triangles always get two names — one by sides, one by angles. You did it!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free