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Identifying Triangles by Their Angles

You can classify triangles by their angles as well as by their sides. The classifications based on angles are as follows:

  • Acute triangle: A triangle with three acute angles (less than 90°).

  • Obtuse triangle: A triangle with one obtuse angle (greater than 90°). The other two angles are acute. If a triangle were to have two obtuse angles (or three), two of its sides would go out in opposite directions and never come together to form a triangle.

  • Right triangle: A triangle with a single right angle (90°) and two acute angles. The legs of a right triangle are the sides touching the right angle, and the hypotenuse is the side across from the right angle.

    (For the three types of triangles based on the length of their sides, see the article, “Identifying Scalene, Isosceles, and Equilateral Triangles.”)

The angles of a triangle add up to 180°. That’s another reason why if one of the angles of a triangle is 90° or larger, the other two angles have to be acute.

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