Triangles
97. Triangle Types by Sides · Scalene, Isosceles, Equilateral
The triangle always closes and side lengths update as you drag.
Triangles are classified by side lengths into three types: equilateral (3 equal sides), isosceles (2 equal sides), and scalene (all 3 sides different). The number of equal sides equals the number of equal angles.
What this lesson covers
Try to break it
Try to stretch the triangle until all three sides are exactly the same length. What name does it get?
How you build it
Build a triangle and classify it by its side lengths.
- Place point A, the first vertex.
- Place point B, the second vertex.
- Place point C, the third vertex.
- Draw the side from A to B.
- Draw the side from B to C.
- Draw the side from C to A to complete the triangle.
The proof, step by step
Prove that the type of a triangle is decided by how many of its sides are equal.
- Scalene: All three sides have different lengths. No symmetry.
- Isosceles: Exactly two sides are equal. The angles opposite them are equal too.
- Equilateral: All three sides are equal. All three angles are 60°.
Worked example
A triangle has side lengths of 6 cm, 6 cm, and 9 cm. How is this triangle classified based on its sides?
Since two sides are equal (6 cm and 6 cm) and one is different (9 cm), it is an Isosceles triangle.
- Scalene
- Isosceles — correct
- Equilateral
- Right-angled