Triangle Properties

A triangle is a polygon with three sides and three angles. It is one of the most fundamental shapes in geometry.

Key Properties of Triangles:

The sum of the interior angles of any triangle is 180°.

The sum of the lengths of any two sides is greater than the third side (Triangle Inequality Theorem).

The exterior angle of a triangle equals the sum of the two opposite interior angles.

Types of Triangles: 

By Sides:

• • Equilateral: All three sides equal, all angles 60°.
  • Isosceles: Two sides equal, base angles equal.
  • Scalene: All sides different, all angles different.

By Angles:

• • Acute: All angles less than 90°.
  • Right: One angle exactly 90°.
  • Obtuse: One angle greater than 90°.

Important Properties & Formulas:

• \( \text{Sum of Angles} = 180^\circ \)
• \( \text{Exterior Angle} = \text{sum of opposite two interior angles} \)
• Area:
  • \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \)
  • Heron’s Formula: \( A = \sqrt{s(s-a)(s-b)(s-c)} \), where \( s = \frac{a+b+c}{2} \)