geometry
Properties of triangles
Compare equilateral, isosceles, scalene and right-angled triangles.
Quick answer
Triangles come in different types, and each type has special properties that make them unique. You can tell what kind of triangle it is by looking at its sides and angles.Learning outcome
By the end of this page, you will be able to identify and describe the properties of four types of triangles: equilateral, isosceles, scalene, and right-angled triangles. Success signs:- You can name the four types of triangles
- You can tell the difference between triangles by looking at their sides and angles
- You can draw each type of triangle
- You can find examples of triangles in everyday life
Why this matters
Understanding triangles is important because they appear everywhere around us! From the roof of your house to the slices of pizza, triangles are used in buildings, art, nature, and even in games and sports. Knowing the properties of triangles helps you solve problems, build things, and understand the world better. This knowledge will also help you in more advanced maths as you grow up.How it works
Triangles are shapes with three straight sides and three angles. There are four main types of triangles, and they are different because of how many sides are the same length and how big their angles are. Let’s look at each one carefully.1. Equilateral triangle
- All three sides are the same length
- All three angles are the same (each is 60°)
2. Isosceles triangle
- Two sides are the same length
- The two angles opposite the equal sides are also equal
3. Scalene triangle
- All three sides are different lengths
- All three angles are different
4. Right-angled triangle
- One angle is exactly 90° (a right angle)
- The side opposite the right angle is called the hypotenuse
Examples you can see
Let’s look at some real examples of triangles so you can see how they work. Equilateral triangle: Imagine a slice of pizza cut into three equal pieces. Each piece is an equilateral triangle because all sides are the same length and all angles are 60°. Isosceles triangle: Think of a roof on a house. Many houses have a roof that looks like an isosceles triangle because two sides are the same length, and the angles on either side of the peak are equal. Scalene triangle: A triangle where no sides are the same length. You can imagine a triangle drawn with sides of 3 cm, 4 cm, and 5 cm. This is a scalene triangle. Right-angled triangle: A triangle with one corner that is exactly 90°. A common example is a corner of a book or a window. The corner where two sides meet at a right angle makes a right-angled triangle.Try it as a mini adventure
Adventure: Triangle Hunt! You are a detective looking for triangles in your home and outside. Here's your mission: 1st time: Look around your room and find something that looks like an equilateral triangle. 2nd time: Find something that looks like an isosceles triangle. 3rd time: Find something that looks like a scalene triangle. 4th time: Find something that looks like a right-angled triangle. 5th time: Draw all four triangles in your notebook and label them. Can you find more than one of each type? Try to think of things like: - A traffic sign (equilateral) - A roof (isosceles) - A piece of paper cut into a triangle (scalene) - A corner of a wall (right-angled)Common mistakes
- Mistake: Thinking that a triangle with two equal sides is always an equilateral triangle. Why it happens: Confusing the definition of equilateral (all three sides equal) with isosceles (two sides equal). Fix: Remember that equilateral means all three sides must be the same, not just two.
- Mistake: Believing that all triangles have one 90° angle. Why it happens: Thinking right-angled triangles are the only kind. Fix: Right-angled triangles are special, but most triangles have different angles.
- Mistake: Drawing a triangle and forgetting to check if the angles add up to 180°. Why it happens: Not knowing that all triangles must have angles that total 180°. Fix: Always remember that the angles in any triangle add up to 180°.
Parent and carer guide
Helping your child understand triangles is fun and simple! Here are some ways you can support their learning:- Practice together: Draw triangles of different types and ask your child to name them.
- Use everyday objects: Point out triangles in your home, like a roof, a slice of pizza, or a traffic sign.
- Play games: Try a triangle sorting game where you place triangle cutouts into the correct category.
- Ask questions: Ask your child to explain how they know a triangle is equilateral or right-angled.
- Don’t worry: It's normal for children to mix up the types at first. Keep practicing and playing with triangles.
Practice questions
- Which triangle has all three sides the same length?
- A) Scalene
- B) Isosceles
- C) Equilateral
- D) Right-angled
- Which triangle has one angle that is exactly 90°?
- A) Isosceles
- B) Scalene
- C) Right-angled
- D) Equilateral
- How many sides are equal in an isosceles triangle?
- A) 1
- B) 2
- C) 3
- D) 0
- Which triangle has all angles different?
- A) Isosceles
- B) Equilateral
- C) Scalene
- D) Right-angled
- What is the total of all angles in any triangle?
- A) 90°
- B) 180°
- C) 270°
- D) 360°
FAQ
What makes a triangle "equilateral"?
An equilateral triangle has three sides that are all the same length and three angles that are all 60°.
Can a triangle be both isosceles and right-angled?
Yes! A triangle can have two equal sides and one 90° angle. This is called an isosceles right triangle.
Are all triangles the same shape?
No, triangles can look very different depending on their sides and angles.
Why do we need to know about triangles?
Triangles are used in building, art, nature, and games. Knowing about them helps us understand and create things.
Can a triangle have more than one right angle?
No, a triangle can only have one right angle because the angles must add up to 180°.