Triangles are a big part of geometry. You can sort them in different ways based on their sides and angles. Knowing about triangles helps solve many math problems. The two main ways to classify triangles are by the lengths of their sides and the size of their angles.

Classification by Sides

1. Scalene Triangle:

   • A scalene triangle has three sides that are all different lengths.
   • For example, if one side is 5 cm, another is 7 cm, and the last one is 10 cm, it is a scalene triangle.
   • In a scalene triangle, no sides or angles are the same, making each one unique.

2. Isosceles Triangle:

   • An isosceles triangle has at least two sides that are the same length.
   • For example, if two sides are 4 cm each and the third side is 6 cm, it is an isosceles triangle.
   • This type of triangle has two equal angles, which are across from the equal sides.
   • There’s a helpful rule called the Isosceles Triangle Theorem that says these angles are the same.

3. Equilateral Triangle:

   • An equilateral triangle is a special kind of isosceles triangle where all three sides are the same length.
   • If all sides are 6 cm long, then it is an equilateral triangle.
   • Also, each angle in an equilateral triangle is 60 degrees.
   • This makes equilateral triangles very balanced and symmetrical.

Classification by Angles

1. Acute Triangle:

   • An acute triangle has all three angles smaller than 90 degrees.
   • For example, angles of 50 degrees, 60 degrees, and 70 degrees make an acute triangle.

2. Right Triangle:

   • A right triangle has one angle that is exactly 90 degrees.
   • A common example is a triangle with angles of 30 degrees, 60 degrees, and 90 degrees.
   • Right triangles are important in trigonometry. They are linked to the Pythagorean theorem, which says: a² + b² = c².

3. Obtuse Triangle:

   • An obtuse triangle has one angle that is bigger than 90 degrees.
   • For example, a triangle with angles measuring 120 degrees, 30 degrees, and 30 degrees is an obtuse triangle.

Combined Classification

A triangle can be sorted in two ways at the same time: by its sides and angles. For example:

• An Isosceles Acute Triangle has two equal sides and all angles that are acute.
• A Scalene Right Triangle has sides that are all different lengths but has one right angle.
• An Equilateral Triangle is also an Acute Triangle because all its angles are 60 degrees.

Conclusion

Triangles can be classified in many ways, mainly by their sides and angles. Understanding if a triangle is scalene, isosceles, or equilateral, as well as whether it is acute, right, or obtuse, is important. This knowledge helps students use different math rules and properties related to triangles. Grasping these ideas is a big part of the Grade 10 math curriculum and helps prepare students for more advanced topics. Knowing about triangle classifications improves students’ overall understanding of geometry and helps them tackle math problems better.