Understanding Obtuse Triangles: Properties and Examples

Obtuse Triangle

A triangle with one obtuse angle

An obtuse triangle is a triangle in which one of the angles measures more than 90 degrees, i.e., an angle in an obtuse triangle is greater than 90 degrees. The other two angles in an obtuse triangle are always acute angles (less than 90 degrees).

The sides opposite to the obtuse angle in an obtuse triangle are the longest sides when compared to the other two sides in the triangle. Since the triangle has an obtuse angle, the longest side will be the one that is opposite to the obtuse angle and the other two sides will be the shorter sides.

Here are some properties of an obtuse triangle:

– An obtuse triangle has only one obtuse angle.
– The sum of the measures of the three angles in an obtuse triangle is always equal to 180 degrees.
– The longest side in an obtuse triangle is always opposite to the obtuse angle.
– An obtuse triangle cannot be equilateral or acute.
– The other two angles are always acute angles.
– An obtuse triangle can be isosceles or scalene.
– The altitude or height of an obtuse triangle falls outside of the triangle.
– The circumcenter of an obtuse triangle is located outside of the triangle.

Example of an obtuse triangle: In the triangle shown below, the angle at vertex A is greater than 90 degrees, making it an obtuse triangle.


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