Classifying Triangles by Side Lengths
Triangles can be classified by the relationships among their side lengths: equilateral triangles have all three sides equal, isosceles triangles have exactly two equal sides, and scalene triangles have all three sides of different lengths. For example, a triangle with sides 7, 7, and 7 is equilateral; one with sides 5, 5, and 8 is isosceles; one with sides 4, 6, and 9 is scalene. This Grade 8 math skill from Yoshiwara Core Math Chapter 1 provides essential vocabulary for describing and categorizing triangles. These classifications connect to angle properties and are foundational for proofs and constructions in geometry.
Key Concepts
Property Triangles can be classified by the lengths of their sides: All three sides of an equilateral triangle are equal in length. In an isosceles triangle, two sides are equal in length. In a scalene triangle, all three sides have different lengths.
Examples A triangle with side lengths of 7 cm, 7 cm, and 7 cm is an equilateral triangle. A triangle with side lengths of 5 inches, 5 inches, and 8 inches is an isosceles triangle. A triangle with side lengths of 4 m, 6 m, and 9 m is a scalene triangle.
Explanation A triangle's name can also come from its side lengths. 'Equilateral' means all sides are equal. 'Isosceles' means two sides are equal. 'Scalene' means no sides are equal—they all have different lengths.
Common Questions
How are triangles classified by side length?
Triangles are classified by side length into three types: equilateral (all three sides equal), isosceles (exactly two sides equal), and scalene (all three sides different).
What is an equilateral triangle?
An equilateral triangle has all three sides equal in length. Because the sides are all equal, all three angles are also equal, each measuring 60 degrees.
What is an isosceles triangle?
An isosceles triangle has exactly two sides of equal length. The two equal sides are called the legs, and the third side is the base. The angles opposite the two equal sides (base angles) are also equal.
When do 8th graders learn to classify triangles?
Students study classifying triangles by side lengths in Grade 8 math as part of Chapter 1 of Yoshiwara Core Math, which covers preliminary geometry concepts.
What is a scalene triangle?
A scalene triangle has all three sides of different lengths. Because all sides are different, all three angles are also different. A scalene triangle has no lines of symmetry.
Can a triangle be both isosceles and equilateral?
Yes, an equilateral triangle can be considered a special case of an isosceles triangle because it has at least two equal sides. However, not all isosceles triangles are equilateral, since an isosceles triangle typically has only two equal sides.