Triangles come in different shapes and sizes. We can group them based on how many sides they have and the angles inside them. Each type has its own special features.

Types Based on Sides:

1. Equilateral Triangle:

   • All three sides are the same length.
   • All three angles are the same, each measuring $60^\circ$.

2. Isosceles Triangle:

   • Two sides are the same length.
   • The angles across from the equal sides are also the same.

3. Scalene Triangle:

   • All three sides are different lengths.
   • All three angles are different, too.

Types Based on Angles:

1. Acute Triangle:

   • All angles are smaller than $90^\circ$.

2. Right Triangle:

   • One angle is exactly $90^\circ$.
   • It follows a special rule called the Pythagorean theorem, which says $a^2 + b^2 = c^2$ (where $c$ is the longest side).

3. Obtuse Triangle:

   • One angle is larger than $90^\circ$.

Summary of Key Facts:

• Equilateral: All angles are $60^\circ$, and all sides are the same.
• Isosceles: Two sides are equal, and two angles are equal.
• Scalene: No sides or angles are equal.
• Right triangles use the Pythagorean theorem to connect the sides.