Classification of Triangles by Side Length

Classification of Triangles Based on Side Lengths

• Triangles are categorized into distinct types depending on the measurements of their sides. There are three primary classifications based on this criteria: equilateral, isosceles, and scalene.

Equilateral Triangle

• A triangle is classified as an equilateral triangle if all three of its sides have the exact same length.

• In an equilateral triangle, if the side lengths are represented by $a$, $b$, and $c$, the relationship between the sides is:

$a = b = c$

Isosceles Triangle

• A triangle is identified as an isosceles triangle when at least two of its sides are equal in length or congruent to one another.

• If a triangle has side lengths $a$, $b$, and $c$, it is isosceles if any two sides satisfy the condition of equality, such as:

$a = b$

Scalene Triangle

• A triangle is defined as a scalene triangle when none of its three sides are equal in length to any other side.

• For a triangle with side lengths $a$, $b$, and $c$, the condition for a scalene triangle is that:

$a \neq b \neq c$

• In such triangles, every side possesses a unique measurement.