Types of Triangles

Learn to identify and classify triangles by their sides and angles.

Elementary20 minLesson
Printable worksheet

Definition

A triangle is a polygon with three sides and three angles. We can classify triangles in two ways:
By Sides:
  • Equilateral: All three sides are equal (a=b=ca = b = c)
  • Isosceles: Exactly two sides are equal
  • Scalene: No sides are equal (all different lengths)
By Angles:
  • Acute: All three angles are less than 90°90°
  • Right: One angle is exactly 90°90°
  • Obtuse: One angle is greater than 90°90°
Sum of angles in any triangle=180°\text{Sum of angles in any triangle} = 180°

Try it now

A triangle has all three sides measuring 7 cm. What type of triangle is this?

Worked Examples

A triangle has sides measuring 5 cm, 5 cm, and 8 cm. What type of triangle is it?

1

List the side lengths

Side 1: 5 cm, Side 2: 5 cm, Side 3: 8 cm → Three sides identified

2

Check if all sides are equal

5≠85 \neq 8, so not all sides are equal → Not equilateral

3

Check if exactly two sides are equal

5=55 = 5, so two sides ARE equal → Two equal sides found

4

Classify the triangle

Two equal sides means isosceles → Isosceles triangle

Common Mistakes

Confusing isosceles with equilateral

Why it's wrong: An equilateral triangle IS technically isosceles (it has at least two equal sides), but we classify it as equilateral because ALL three sides are equal.

Correct: Equilateral = all 3 sides equal. Isosceles = exactly 2 sides equal.

Thinking a right triangle can also be obtuse

Why it's wrong: A triangle can only have ONE angle that is 90°90° or greater. If one angle is 90°90°, the other two must be acute (less than 90°90°).

Correct: A triangle is right, acute, OR obtuse - never two of these at once.

Forgetting that angles sum to 180°180°

Why it's wrong: Students sometimes add angles incorrectly or forget this rule when finding missing angles.

Correct: Always check: angle 1 + angle 2 + angle 3 = 180°180°

Interactive Visual

Triangle Explorer

By sides:Isosceles
By angles:Acute

Area:

20,000.0 sq units

Drag vertices to create different triangle types.

Interactive Sandbox

Expression Calculator

Try these:

History

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Practice Problems

18 problems
Problem 1 of 18
Easy

A triangle has all three sides measuring 7 cm. What type of triangle is this?

Why It Matters

Triangles are everywhere in the world around us:
  • Architecture: The Eiffel Tower uses thousands of triangles for strength and stability
  • Engineering: Bridges often use triangular supports because triangles don't collapse under pressure
  • Nature: Pyramids in Egypt, slices of pizza, and even the shape of mountains
  • Sports: The warning triangle on the road, yield signs, and pool rack formations
Understanding triangle types helps architects, engineers, and artists design stable and beautiful structures!

Real World Applications

Architecture and Construction

Architects and engineers use triangles because they are the most stable shape. Unlike rectangles, triangles cannot be pushed out of shape without breaking a side.

Example:

The roof of most houses forms a triangle (often isosceles) to let rain and snow slide off.

1Try It Yourself

A house roof has two equal sides of 5 meters each and a base of 8 meters.

What type of triangle is the roof?

Step 1: Write the mathematical expression

Compare the sides: 5 m, 5 m, 8 m

Musical Instruments

The triangle instrument used in orchestras is actually an equilateral triangle bent from a metal rod.

Example:

A musical triangle has all three sides of equal length (usually about 15-20 cm each) so it produces a clear, resonant tone.

2Try It Yourself

A musical triangle has sides of 18 cm, 18 cm, and 18 cm.

What type of triangle is this?

Step 1: Write the mathematical expression

Check if all sides are equal

Road Signs

Warning signs on roads are triangular to catch drivers' attention. The triangle shape is recognized internationally.

Example:

Yield signs in many countries use an equilateral triangle (pointing down) or an isosceles triangle.

3Try It Yourself

A yield sign has angles of 60°60°, 60°60°, and 60°60°.

What type of triangle is it by angles?

Step 1: Write the mathematical expression

Compare each angle to 90°90°

Key Takeaways

  • 1Triangles can be classified by sides: equilateral (3 equal), isosceles (2 equal), scalene (0 equal)
  • 2Triangles can be classified by angles: acute (all < 90°90°), right (one = 90°90°), obtuse (one > 90°90°)
  • 3Every triangle has angles that sum to exactly 180°180°
  • 4A triangle can have TWO classifications (one by sides, one by angles), like 'acute isosceles'

Frequently Asked Questions

No. A triangle can only have ONE angle that is 90°90° or greater. If it has a right angle (90°90°), the other two angles must be acute. If it has an obtuse angle (> 90°90°), the other two must be acute.
No. A triangle can only have ONE angle that is 90°90° or greater. If it has a right angle (90°90°), the other two angles must be acute. If it has an obtuse angle (> 90°90°), the other two must be acute.
Technically yes! An equilateral triangle has three equal sides, which means it definitely has 'at least two' equal sides. However, we use the more specific term 'equilateral' when all three sides are equal.
Scalene triangles are actually the most common in nature and random drawings, because it's rare for sides to be exactly equal. However, isosceles and right triangles are very common in human-made structures.

Glossary

Equilateral triangle
A triangle with all three sides of equal length and all angles equal to 60°60°
Isosceles triangle
A triangle with exactly two sides of equal length
Scalene triangle
A triangle with no equal sides (all three sides have different lengths)
Acute triangle
A triangle where all three angles are less than 90°90°
Right triangle
A triangle with one angle that measures exactly 90°90°
Obtuse triangle
A triangle with one angle greater than 90°90°
Vertex
A corner point of a triangle where two sides meet
Base
The bottom side of a triangle (any side can be chosen as the base)

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