Detailed definition
Understanding Obtuse Triangle
Obtuse Triangle is a triangle with one interior angle greater than ninety degrees. An obtuse triangle has one angle greater than 90 degrees. Since the interior angles of a triangle sum to one hundred eighty degrees, the other two angles must both be acute.
An obtuse triangle is significant because one wide angle changes several geometric features at once. The longest side lies opposite the obtuse angle, and some triangle centers move outside the triangle.
This type is important in classification and theorem work because many statements about heights, centers, or perpendicular constructions behave differently once the triangle becomes obtuse.
Key facts
Important ideas to remember
- An obtuse triangle has one angle greater than 90 degrees.
- Only one angle in a triangle can be obtuse because the interior angles sum to one hundred eighty degrees.
- The longest side lies opposite the obtuse angle.
- In an obtuse triangle, the orthocenter and circumcenter lie outside the triangle.
Where it is used
Where obtuse triangle shows up
- Use obtuse-triangle classification when comparing angle types in triangle problems.
- Use it in center-location discussions and altitude constructions.
- Use it to decide which geometric case applies before using a theorem or proof step.
Common mistakes
What to watch out for
- Do not call a triangle obtuse unless one interior angle is actually greater than ninety degrees.
- Do not forget that the other two angles must then remain acute.
- Do not assume the widest-looking side is opposite the largest angle unless the figure has been read carefully.