Classifying Triangles Lesson: Types by Sides and Angles

Lesson Overview

• What Is a Triangle?
• Classifying Triangles by Side Lengths
• Classifying Triangles by Angle Measures
• Triangle Angle Rule: Always Adds to 180°

In geometry, one of the most important shapes is the triangle. A triangle is a closed shape with three straight sides and three angles. Although all triangles have the same number of sides and angles, they don't all look the same.

Triangles come in different types, and we can classify them based on:

• The lengths of their sides
  
• The sizes of their angles
  

In this lesson, you'll learn how to:

• Identify triangles by side length and angle measure
  
• Understand and apply the 180° rule for triangle angles
  
• Recognize that a triangle can belong to more than one category
  
• Use drawings and clues to build or describe different triangle types
  

What Is a Triangle?

A triangle is a two-dimensional shape with the following features:

• 3 straight sides
  
• 3 angles
  
• 3 vertices (corners)
  

The three angles inside any triangle always add up to 180 degrees. This is known as the triangle angle sum rule and it works for every triangle, no matter the type.

Example:

If two angles in a triangle are 45° and 60°, then the third angle is:
180° − (45° + 60°) = 75°
→ All three angles: 45°, 60°, 75°

This rule is very useful for finding missing angles in a triangle when two are already given.

Classifying Triangles by Side Lengths

The side lengths of a triangle help us divide them into three groups.

🔺 Scalene Triangle

• All three sides are different
  
• All three angles are also different
  

Example:

If the sides are 6 cm, 5 cm, and 4 cm, none are equal.
→ This is a scalene triangle

Scalene triangles are the most irregular. You often find them in real-world shapes that don't have any equal sides.

🔺 Isosceles Triangle

• Two sides are equal
  
• The two angles opposite those equal sides are also equal
  

Example:

Sides = 5 cm, 5 cm, 3 cm
→ Two equal sides → Isosceles triangle

This type of triangle often looks symmetrical and stands evenly on one side.

🔺 Equilateral Triangle

• All three sides are equal
  
• All angles are 60°
  

Example:

Sides = 7 cm, 7 cm, 7 cm
→ All equal → Equilateral triangle

Equilateral triangles are perfectly balanced and have three equal corners too.

Classifying Triangles by Angle Measures

The angles inside a triangle also help us classify it into three more types.

Acute Triangle

• All three angles are less than 90°
  
• Sharp-looking, often small and pointy
  

Example:

Angles = 50°, 60°, 70°
→ All less than 90° → Acute triangle

This is the most common triangle type in designs and art.

Right Triangle

• Has exactly one 90° angle
  
• The other two angles add up to 90°
  

Example:

Angles = 90°, 40°, 50°
→ One right angle → Right triangle

The right triangle is very useful in real-world structures like stairs, ramps, and buildings.

Obtuse Triangle

• Has one angle greater than 90°
  
• The other two are smaller than 90°
  

Example:

Angles = 110°, 35°, 35°
→ One angle over 90° → Obtuse triangle

An obtuse triangle always looks wider on one side due to its large angle.

Take This Quiz:

Triangle Angles and Measurements

Triangle Angle Rule: Always Adds to 180°

This rule is true for every triangle:

The sum of all three interior angles is exactly 180 degrees

You can use this rule to find a missing angle if the other two are known.

Example 1:

Two angles are 70° and 50°
Missing angle = 180° − (70 + 50) = 60°

Example 2:

One angle is 90°, another is 30°
Missing angle = 180° − (90 + 30) = 60°

This rule helps you solve for unknowns and check your answers.

Can a Triangle Be More Than One Type?

Yes! A triangle can belong to more than one category at the same time.

🔸 Multiple Classifications:

• A triangle can be equilateral and also acute, because all angles are 60°, which are less than 90°.
  
• A triangle can be isosceles and right, if it has two equal sides and one 90° angle.
  
• A triangle can be scalene and obtuse, if all sides and angles are different, and one angle is more than 90°.
  

So, it's common to see one triangle described using both side and angle categories.

Tip:

Side-based names (scalene, isosceles, equilateral) describe the lengths.
Angle-based names (acute, right, obtuse) describe the angles.

Take This Quiz:

Types of Triangles Quiz Questions

Using Side Lengths to Predict Angles

Although you can't measure an angle just by looking at the sides, certain clues can help:

• Short sides often create small angles
  
• Longer side opposite an angle usually means a larger angle
  
• In an equilateral triangle, all angles are the same (60°)
  
• In a scalene triangle, all angles are different
  

Example:

In triangle ABC:

• AB = 5 cm
  
• BC = 8 cm
  
• AC = 9 cm
  

This triangle is scalene. Since AC is the longest side, the angle opposite AC will be the largest.

Knowing how side lengths relate to angle size helps when sketching triangles or identifying types.

Drawing and Describing Triangles

Drawing triangles is not just fun-it helps you understand how angle and side combinations create different triangle types.

Steps to Draw a Triangle:

1. Start by drawing the base (any side)
   
2. Use a protractor to measure and draw angles
   
3. Finish the shape by connecting all sides
   

Example:

Draw a triangle with angles 60°, 60°, and 60°
→ All angles equal = equilateral triangle

Draw a triangle with sides 6 cm, 6 cm, and 4 cm
→ Two sides equal = isosceles triangle

Try drawing one of each triangle type to practice classification!

Take This Quiz:

Geometry ---- Classifying Triangles 10/17/09