Types of triangles

Types of triangles may be classified by their sides, by their angles or by a combination of both sides and angles.
Types of triangles

Types of triangles classified by their sides only.

A triangle classified by its sides only can either be scalene, isosceles, or equilateral.

Scalene triangle: A scalene triangle is a triangle that has no equal sides. The following is a scalene triangle.
Scalene triangle
Isosceles triangle: An isosceles triangle is a triangle that has two equal sides. The following is an isosceles triangle.

Isosceles triangle
Equilateral triangle: An equilateral triangle is a triangle that has three equal sides. The following is an equilateral triangle.

Equilateral triangle

Types of triangles classified by their angles only.

A triangle classified by its angles only can either be acute, right, or obtuse.

Right triangle: A right triangle has a 90 degrees angle.The following is a right triangle.

Right triangle
Obtuse triangle: An obtuse triangle has only one angle that is bigger than 90 degrees (Obtuse angle). The following is an obtuse triangle.

Obtuse triangle
Acute triangle: In an acute triangle, all angle are less than 90 degrees, so all angles are acute angles.The following is an acute triangle.

Types of triangles classified by their sides and angles

We can also name triangles using angles and sides at the same time.

If a triangle has one right angle and two equal sides, we can call that triangle right isosceles triangle.

If a triangle has only acute angles and no equal sides, we can call that triangle acute scalene triangle.

If a triangle has one right angle and no equal sides, we can call that triangle right scalene triangle.

If a triangle has only acute angles and two equal sides, we can call that triangle acute isosceles triangle.

If a triangle has two equal sides and one obtuse angle, we can call that triangle obtuse isosceles triangle.

If a triangle has three equal sides and only acute angles, we can call that triangle acute equilateral triangle.

If a triangle has no equal sides and one obtuse angle, we can call that triangle obtuse scalene triangle.

Is it possible to have an obtuse equilateral triangle?

No it is not possible. A triangle cannot be obtuse and equilateral at the same time. An equilateral triangle cannot have an obtuse angle because all 3 angles in an equilateral triangle measure 60 degrees.

Is it possible to have a right equilateral triangle?

If the triangle is a right triangle, then one of the three angles is equal to 90 degrees. The sum of the other two angles must then add up to 90 degrees. This makes it impossible for all three angles to be equal.

Types of triangles quiz. Take the quick to check if you understand this lesson.

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