Grade 8 geometry lesson
Obtuse Triangle: Definition, Examples, Angle Rule, and Practice
An obtuse triangle is a triangle with one obtuse angle inside it.
What is an obtuse triangle?
An obtuse triangle is a triangle with one wide inside angle.
That wide angle is more than 90° and less than 180°.
The triangle is named obtuse because it contains one obtuse angle.
Obtuse triangle rule
A triangle can be obtuse only when one of its three angles is obtuse.
One triangle angle is more than 90° and less than 180°.
Because angles in a triangle add to 180°, the other two angles must be acute.
Why only one angle can be obtuse
A triangle has only 180° total inside.
If one angle is already more than 90°, less than 90° is left for the other two angles together.
That means a triangle cannot have two obtuse angles.
Triangle type chart
Triangles can be named by their angle sizes.
An acute triangle has three acute angles. A right triangle has one 90° angle. An obtuse triangle has one angle greater than 90°.
These names are about angle size, not side length.
Worked example
Problem: A triangle has angles 118°, 34°, and 28°. What type of triangle is it?
Step 1: Look for an angle greater than 90°.
Step 2: 118° is greater than 90° and less than 180°.
Step 3: A triangle with one obtuse angle is an obtuse triangle.
Answer: The triangle is an obtuse triangle.
Obtuse triangles and height
An obtuse triangle can look stretched because one corner opens wide.
When you study area, the height of an obtuse triangle may fall outside the triangle.
Review altitude of a triangle to see how perpendicular height works for obtuse triangles.
Common mistakes
Do not call a triangle obtuse just because it looks long. Check the angle measures.
Do not call 90° obtuse. A triangle with one 90° angle is a right triangle.
Do not expect two obtuse angles in one triangle. The three inside angles only add to 180°.
Quick practice
1. A triangle with angles 100°, 40°, and 40° is obtuse.
2. A triangle with angles 90°, 50°, and 40° is right, not obtuse.
3. A triangle with angles 70°, 60°, and 50° is acute.
4. An obtuse triangle has exactly one obtuse angle.
Interactive playground
Build an obtuse triangle
Change the wide angle. The other two angles stay acute because the triangle total is 180°.