Triangles are classified into different types based on the lengths of their sides and the measures of their angles. The three main types of triangles are:

Equilateral Triangle: An equilateral triangle has all three sides of equal length and all three angles measuring 60 degrees. It is the most symmetrical type of triangle. Properties:

All three sides are congruent (equal in length).

All three angles measure 60 degrees.

Isosceles Triangle: An isosceles triangle has two sides of equal length and two angles of equal measure. Properties:

At least two sides are congruent.

At least two angles are equal in measure.

Scalene Triangle: A scalene triangle has all three sides of different lengths, and all three angles are of different measures. Properties:

All three sides have different lengths.

All three angles have different measures.

These classifications are based on side lengths and angle measures and provide a basic understanding of triangle types. Triangles can also be categorized based on their angles into acute, obtuse, or right triangles:

Acute Triangle: All three angles are less than 90 degrees.

Obtuse Triangle: One angle is greater than 90 degrees.

Right Triangle: One angle is exactly 90 degrees (forming a right angle). In a right triangle, the side opposite the right angle is called the hypotenuse.