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Classification of Triangles (On the Basis of Sides, and of Angles) - Obtuse Angled Triangle

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definition

Obtuse angled Triangle: An obtuse triangle is one that has an angle greater than 90°.

notes

Obtuse angled Triangle:

  • An obtuse triangle is one that has an angle greater than 90°. Because all the angles in a triangle add up to 180°, the other two angles have to be acute (less than 90°). It's impossible for a triangle to have more than one obtuse angle.

                       

Properties of obtuse triangles:

  • Whenever a triangle is classified as obtuse, one of its interior angles has a measure between 90 and 180 degrees.
  • An obtuse triangle has only one angle greater than 90° since the sum of the angles in any triangle is 180°. If one of the angles is greater than 90°, then the sum of the other two angles must be less than 90°, so the other two angles must both be acute angles.

               

      For △DEF above, ∠D + ∠F = 60° < 90°, so ∠D and ∠F are acute angles.

  • The side opposite the obtuse angle for an obtuse triangle is the longest side of the triangle. The greater the angle, the longer the side opposite it. Conversely, the longer the side, the greater the angle opposite it.
  • An obtuse triangle may be either isosceles (two equal sides and two equal angles) or scalene (no equal sides or angles).
  • The orthocenter is the point where all three altitudes of the triangle intersect. The orthocenter of an obtuse triangle is located outside of the triangle.
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