Classifying Triangles by Sides and Angles

Grade 4 Medium Geometry

Learning Objectives

Identify scalene, isosceles, and equilateral triangles
Distinguish acute, right, and obtuse angles in triangles

Concept Explanation

Triangles can be classified by their sides or angles. By sides:

Scalene: all sides different
Isosceles: two sides the same
Equilateral: all sides equal

By angles:

Acute: all angles < 90°
Right: exactly one 90° angle
Obtuse: exactly one angle > 90°

Learning these distinctions builds deeper understanding of geometric properties and how shapes can be categorized.

Worked Examples

Example 1

Problem: A triangle has sides of 3 cm, 3 cm, and 5 cm. What type is it by side length?
Solution: Isosceles
Explanation: Two sides are equal (3 cm and 3 cm).

Example 2

Problem: If a triangle has a 90° angle, what is it called by angle measure?
Solution: Right triangle
Explanation: Exactly one 90° angle defines a right triangle.

Example 3

Problem: A triangle has sides 4 cm, 4 cm, 4 cm. Classify it.
Solution: Equilateral (and acute)
Explanation: All sides are the same, and all angles in an equilateral triangle are 60° (acute).

Common Errors

Error	Correction	Reason
Mixing up isosceles and scalene	Check if at least two sides are equal	Isosceles has two equal sides; scalene has none.
Assuming right angles without measuring	Use a protractor or known properties	Just because a triangle “looks right” doesn’t guarantee a 90° angle.
Forgetting equilateral triangles are also equiangular	Each angle in an equilateral triangle is 60°	Understanding angles and sides go hand in hand in equilateral triangles.

Practice Problems

Problem: A triangle has side lengths 5 cm, 7 cm, and 7 cm. Classify by sides.
Solution: Isosceles
Problem: A triangle with a 100° angle is what type by angles?
Solution: Obtuse
Problem: All three sides are different. What is the triangle called by side length?
Solution: Scalene
Problem: A 90° angle in a triangle indicates what type?
Solution: Right triangle
Problem: Sides of 2, 2, 2. Classify completely.
Solution: Equilateral (also acute)

Real-World Application Example

Architects often use triangular supports for strength in structures. Knowing which triangles are best (like right or equilateral) helps ensure stability and proper design in bridges and rooftops.