Classify Triangles by Angle Type

Students classify triangles as acute (all angles less than 90°), right (one angle exactly 90°), or obtuse (one angle greater than 90°) based on their angles. Students measure or estimate angle sizes and justify classifications.

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Grade 4 · Classifying Two-Dimensional Figures · question 1 of 3

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20 rungs. A star at the top.

Triangle CDE is drawn. Which kind fits?

right triangle

obtuse triangle

acute triangle

How it is taught

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A triangle is named by its largest angle.

An obtuse triangle has one angle over 90.

An acute triangle has all angles under 90.

Read it: A triangle is named by its biggest angle

Triangle ABC has a square corner at A, so its biggest angle is a right angle and it is a right triangle.

Find the biggest angle: the vertex where the 2 sides open widest.
Compare it with a square corner: narrower is acute, the square is right, wider is obtuse.
Name the triangle by that angle: acute, right or obtuse.

At most 1 angle of a triangle can be right or obtuse; the other 2 are always acute.

Every triangle has at least 2 acute angles, so they cannot tell triangles apart.

Only the biggest angle can be right or obtuse, so it decides the name.

Look at the biggest angle and name the triangle by it.

Calling triangle ABC acute because 2 of its angles are acute.

Every triangle has 2 acute angles. Its biggest angle, at A, is a square corner, so it is a right triangle.

A triangle's angles are 35°, 40° and 105°. What kind of triangle is it? — an obtuse triangle. Its biggest angle, 105°, is more than 90°, so it is an obtuse triangle.

Right vs Acute vs Obtuse

Today we'll sort triangles by their angles.

Here are three triangles. Let's check the biggest angle in each one.

Grade 4 · Naming triangles by their biggest angle

The first triangle has a square corner — that's exactly ninety degrees.

When a triangle has a ninety-degree angle, we call it a right triangle.

In the middle triangle, every angle is smaller than ninety degrees.

All three angles less than ninety? That's an acute triangle.

The last triangle has one angle that's wider than ninety degrees.

One angle bigger than ninety makes it an obtuse triangle.

Right, acute, or obtuse — every triangle gets its name from its biggest angle!

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.

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Standard

CCSS.4.G.A.2

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size

Grade 4

Quoted from the Common Core State Standards.

Where this sits

Comes after

Leads to

Classify Quadrilaterals Using Parallel and Perpendicular Lines

What a star here means

A star here is the top of a twenty-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 4

This is one rung of 71 in Grade 4 mathematics, in the order they build on each other.

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