Scalene triangle
A scalene triangle is a triangle with no sides of equal length and no angles of equal measure — every side and every angle is different. In a scalene triangle, all three sides might measure 5, 7, and 9 cm, and the corresponding angles (opposite the longer sides are the larger angles) are all distinct. This Grade 7 math skill from Saxon Math, Course 2 is part of triangle classification alongside equilateral (all sides equal) and isosceles (exactly two sides equal), and knowing these categories builds the vocabulary needed for triangle congruence and similarity theorems.
Key Concepts
Property A scalene triangle has all sides of different lengths and all angles of different measures.
Examples A triangle with side lengths of 5 cm, 7 cm, and 8 cm is a scalene triangle. A triangle with angles measuring $30^\circ$, $60^\circ$, and $90^\circ$ is a scalene triangle.
Explanation Meet the scalene triangle, the king of being unique! Every side has a different length, which means every angle has a different measure. No repeats, no matches, just three different sides and angles.
Common Questions
What is a scalene triangle?
A scalene triangle has no sides of equal length and no angles equal. All three sides and all three angles have different measures.
How is a scalene triangle different from isosceles and equilateral triangles?
An equilateral triangle has all three sides equal. An isosceles triangle has exactly two sides equal. A scalene triangle has no sides equal — all three are different lengths.
What are the angle properties of a scalene triangle?
A scalene triangle has no equal angles. However, like all triangles, its three interior angles always sum to 180 degrees.
Can a scalene triangle be a right triangle?
Yes. A right scalene triangle has one 90-degree angle and two unequal acute angles. The 3-4-5 right triangle is a common example.
When do students learn about scalene triangles?
Triangle classification is typically introduced in Grade 4-5 and reviewed in Grade 7. Saxon Math, Course 2 covers scalene triangles in Chapter 8 as part of the geometry vocabulary.
How do you identify a scalene triangle?
Measure all three sides (or all three angles). If no two measurements are equal, the triangle is scalene.
How does triangle classification connect to congruence?
When proving triangles congruent using criteria like SSS or SAS, understanding triangle classification (scalene vs isosceles vs equilateral) helps determine which sides and angles to compare.