Scalene triangle
High School
Definition
A triangle with three unequal lengths and angles. Scalene triangles can have a right angle with 2 acute angles, 3 acute angles, or an obtuse angle and 2 acute angles. The angles of any triangle must add up to 180°.
Worked examples
\(\)Triangle with sides \( 3, 4, 5 \) cm and angles \( 37°, 53°, 90°\)
All three sides differ, all three angles differ — this right scalene triangle has no equal parts.
\(\)Triangle with sides \( 5, 7, 9 \) cm and angles \( 33.6°, 50.7°, 95.7°\)
An obtuse scalene triangle: all sides unequal, all angles unequal, one angle greater than 90°.
\(\)Triangle with sides \( 6, 8, 10 \) m and angles \( 36.9°, 53.1°, 90°\)
Even though this is a 3-4-5 scaled up, sides are unequal so it remains scalene.
Common mistakes
- A scalene triangle must be obtuse → A scalene triangle can be acute, right, or obtuse Scalene only means all sides differ; the angle types can vary.
- Triangle with sides \(5, 5, 7\) is scalene → That triangle is isosceles because two sides are equal Scalene requires all three sides to be different lengths.
- If angles are \(60°, 60°, 60°\) and sides differ, it's scalene → Equal angles force equal sides; this is equilateral, not scalene A triangle with all equal angles must have all equal sides.
Where you'll use it next
You'll classify scalene triangles when solving for unknown sides and angles using the Law of Sines and Law of Cosines in trigonometry, and when analyzing geometric proofs and real-world structures in geometry and beyond.
Found in 1 StudyPug lesson
Mastering Triangle Classification: Your Key to Geometry Success
10th Grade10thGeometry
Unlock the world of geometry by mastering triangle classification. Learn to identify and understand various triangle types, their properties, and real-world applications. Boost your problem-solving skills today!
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026