Grade 4 (age 9-10)

grade 4 Types of Triangles

A triangle has three sides and three angles. Sorted by side lengths, there are equilateral triangles with all three sides equal, isosceles triangles with two equal sides, and scalene triangles with no equal sides. Sorted by angles, there are acute triangles with three acute angles, right triangles with one right angle and obtuse triangles with one obtuse angle, and in every triangle the three angles add up to 180°. Choose a triangle with the buttons; each corner shows its angle, so you can check that the three angles add up to 180°.

Two Ways to Sort Triangles

🔺 Two Ways to Sort Triangles

①By side lengths: equilateral, isosceles and scalene triangles

②By angles: acute, right and obtuse triangles

③One triangle belongs to a group in each way at once; a right triangle with two equal sides is a right isosceles triangle

④In every triangle, the three angles add up to 180°

Comparing Triangles

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Sorting by Side Lengths

📏 Sides and Angles Together

①An equilateral triangle has three equal sides, and its three angles are all 60°

②An isosceles triangle has two equal angles opposite its two equal sides; in the picture these base angles are 70° each

③If all three sides are different, all three angles are different too

④In an acute triangle all three angles must be acute; one acute angle is not enough

⑤A triangle can have at most one right angle or one obtuse angle

Summary

Equilateral Triangle

Three equal sides, each angle = 60°

With every angle at 60°, it is also an acute triangle

Right Triangle

One angle = 90°

The two sides that form the right angle are perpendicular

Angle Sum of a Triangle

Sum of the three angles = 180°

Always 180°, whatever the shape or size

🎯 Summary

①By sides: equilateral (three equal), isosceles (two equal), scalene (none equal)

②By angles: acute (all acute), right (one right angle), obtuse (one obtuse angle)

③The three angles always add up to 180°

④An equilateral triangle also has two equal sides, so it counts as isosceles too

⑤In a right triangle, the longest side is the one opposite the right angle

Examples and Unit Test

Example 1

What is a triangle with all three sides equal called, and how large is each of its angles?

A triangle with three equal sides is equilateral, and its three angles are equal too.

Splitting the 180° angle sum into three equal parts gives 180° ÷ 3 = 60°.

▸ Equilateral triangle, each angle 60°

With every angle at 60°, an equilateral triangle is also an acute triangle.

Example 2

What is a triangle with two equal sides called?

Sort the triangle by its side lengths.

A triangle with two equal sides is an isosceles triangle.

▸ Isosceles triangle

An equilateral triangle also has two equal sides, so it counts as isosceles too.

Unit Test

What is a triangle with one 90° angle called?

①Acute triangle

②Right triangle

③Obtuse triangle

④Equilateral triangle

▸ ② Right triangle

Sort the triangle by its angles.

A triangle with one right angle (90°) is a right triangle.

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Angles

Types of Quadrilaterals

Last updated 2026-10-17