October 4, 2025

What Is The Difference Between Equilateral Isosceles And Scalene Triangles

Q: Can a triangle be both right-angled and isosceles?

Yes. A right-angled isosceles triangle has one 90° angle and two 45° angles. The two sides that form the right angle are equal in length.

Q: What is an equiangular triangle?

An equiangular triangle is another name for an equilateral triangle. It specifically means that all three of its internal angles are equal, which forces all three sides to be equal as well.

Q: Can an equilateral triangle be a right triangle?

No. An equilateral triangle must have three 60° angles to be equiangular. A right triangle must have one 90° angle, so the two definitions cannot apply to the same triangle.

Q: Is a scalene triangle always obtuse?

No, this is a common misconception. A scalene triangle can be acute (all angles less than 90°), right (one 90° angle), or obtuse (one angle greater than 90°), as long as all three side lengths are different.

Learn the key differences between equilateral, isosceles, and scalene triangles based on their side lengths and angle measurements. A simple guide for students.

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Defining Triangles by Side Length

Equilateral, isosceles, and scalene are terms used to classify triangles based on the length of their sides. An equilateral triangle has three equal-length sides. An isosceles triangle has two equal-length sides. A scalene triangle has no equal-length sides; all three are different.

Section 2: Relationship Between Sides and Angles

The side lengths of a triangle directly determine its angles. An equilateral triangle is also 'equiangular,' meaning it has three equal 60° angles. An isosceles triangle has two equal angles opposite its two equal sides. A scalene triangle has three angles of different measurements, corresponding to its three different side lengths.

Section 3: A Practical Example

Think of a standard triangular yield sign; its three equal sides make it an equilateral triangle. A slice of pizza often forms an isosceles triangle, with the two crustless sides being equal in length. A shard of broken glass with three straight, uneven edges is a perfect real-world example of a scalene triangle.

Section 4: Why This Classification is Important

Classifying triangles is a fundamental concept in geometry that allows us to understand their properties and solve problems. This classification helps in calculating area, perimeter, and angles, and forms the basis for more advanced topics like trigonometry, engineering, and architectural design.

Frequently Asked Questions

Can a triangle be both right-angled and isosceles?

What is an equiangular triangle?

Can an equilateral triangle be a right triangle?

Is a scalene triangle always obtuse?