Triangles are a fundamental shape in geometry, characterized by three sides and three angles. Here’s an overview of their properties, types, and applications: Properties of Triangles Sum of Angles : The sum of the interior angles of a triangle is always 180 degrees. Types of Sides : Equilateral Triangle : All three sides are equal, and each angle measures 60 degrees. Isosceles Triangle : Two sides are equal, and the angles opposite those sides are also equal. Scalene Triangle : All sides and angles are different. Types of Angles : Acute Triangle : All angles are less than 90 degrees. Right Triangle : One angle is exactly 90 degrees. Obtuse Triangle : One angle is greater than 90 degrees. Area : The area A A of a triangle can be calculated using the formula: A = 1 2 × base × height A = 2 1 × base × height Alternatively, for a triangle with sides of length a a , b b , and c c , Heron's formula can be used: A = s ( s − a ) ( s − b ) ( s − c ) A = s ( s − a )...