Classify triangles by properties
Theory
A triangle can be named by its sides — equilateral, isosceles or scalene — and by its angles — acute, right or obtuse. Count the equal sides, check the largest angle, and remember the three angles always add to \(180^\circ\).
A triangle is a shape with three straight sides and three angles. It can be named in two ways.
By its sides: an equilateral triangle has three equal sides, an isosceles triangle has exactly two equal sides, and a scalene triangle has no equal sides.
By its angles: an acute triangle has all three angles less than \(90^\circ\), a right triangle has one \(90^\circ\) angle, and an obtuse triangle has one angle greater than \(90^\circ\).
Tick marks on a drawing show which sides are equal. The three angles of any triangle add to \(180^\circ\).
The angle names sort a triangle by its largest angle.
| Type | Largest angle | Example angles |
|---|---|---|
| Acute | less than \(90^\circ\) | \(70^\circ, 60^\circ, 50^\circ\) |
| Right | exactly \(90^\circ\) | \(90^\circ, 60^\circ, 30^\circ\) |
| Obtuse | more than \(90^\circ\) | \(110^\circ, 40^\circ, 30^\circ\) |
How to classify a triangle
- Count the equal sides. Three equal is equilateral, two equal is isosceles, none equal is scalene.
- Look at the angles. All under \(90^\circ\) is acute, one \(90^\circ\) is right, one over \(90^\circ\) is obtuse.
- Check the angle sum. A missing angle is \(180^\circ\) take away the other two.
Exactly two sides are equal, so the triangle is isosceles.
| \(180^\circ - 55^\circ - 65^\circ\) | \(=\) | \(60^\circ\) |
One angle is \(90^\circ\), so the triangle is right-angled.
| \(80^\circ + 60^\circ + 50^\circ\) | \(=\) | \(190^\circ\) |
That is not \(180^\circ\), so no.
Common pitfalls
Frequently asked questions
What are the three types of triangle by sides?
Equilateral has three equal sides, isosceles has exactly two equal sides, and scalene has no equal sides.
How do you name a triangle by its angles?
Look at the biggest angle. All angles under \(90^\circ\) is acute, one angle of \(90^\circ\) is right, and one angle over \(90^\circ\) is obtuse.
Do the angles of a triangle always add to 180 degrees?
Yes. Every triangle has angles that add to \(180^\circ\), so a missing angle is \(180^\circ\) minus the other two.
Can a triangle be isosceles and right-angled?
Yes. Side names and angle names describe different things, so a triangle can have two equal sides and also a \(90^\circ\) angle.
What do the tick marks on a triangle mean?
Sides with the same number of ticks are equal in length. Three matching ticks means equilateral, two matching ticks means isosceles.