Triangles can be classified based on both their sides and their angles. The classification by sides involves looking at the lengths of the three sides of the triangle, while the classification by angles considers the measures of the three angles inside the triangle.
Classification by Sides:
- Equilateral Triangle:
All three sides are of equal length. All three angles are also equal, each measuring 60 degrees.
- Isosceles Triangle:
Two sides are of equal length, and the third side is of a different length. The angles opposite the equal sides are also equal.
- Scalene Triangle:
All three sides have different lengths. All three angles are also different.
Classification by Angles:
- Acute-angled Triangle:
All three angles are acute (less than 90 degrees).
- Right-angled Triangle:
One angle is a right angle (exactly 90 degrees). The side opposite the right angle is called the hypotenuse, and the other two sides are the legs. The Pythagorean theorem holds for right-angled triangles.
- Obtuse-angled Triangle:
One angle is obtuse (greater than 90 degrees).
