Classify triangles

key notes :

Classification by Sides

  • Equilateral Triangle: All three sides are equal. All angles are also equal, measuring 60° each.
  • Isosceles Triangle: Two sides are equal in length, and the angles opposite these sides are equal.
  • Scalene Triangle: All three sides are of different lengths, and all three angles are of different measures.

Classification by Angles

  • Acute Triangle: All three angles are less than 90°.
  • Right Triangle: One angle is exactly 90°.
  • Obtuse Triangle: One angle is greater than 90° but less than 180°.

Properties of Triangles

  • Sum of Angles: The sum of the interior angles of any triangle is always 180°.
  • Exterior Angle Theorem: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Examples of Classification

  • An equilateral triangle is also acute since all angles are 60°.
  • An isosceles triangle can be right, acute, or obtuse depending on the angles.
  • A scalene triangle can also be right, acute, or obtuse based on the angle measures.

Learn with an example

A triangle has angle measurements of 86°, 77° and 17°. What kind of triangle is it?

  • acute
  • right
  • obtuse

This triangle is an acute triangle. All 3 angles are less than 90°.

What kind of triangle is this?

  • equilateral
  • isosceles but not equilateral
  • scalene

Look at this triangle:

This triangle is isosceles but not equilateral. 2 angles are the same, but the third angle is different.

A triangle has angle measurements of 90°, 16° and 74°. What kind of triangle is it?

  • acute
  • right
  • obtuse

This triangle is a right triangle. The 90° angle is a right angle.

Let’s practice!