Properties of Triangle (original) (raw)

Last Updated : 11 Feb, 2026

A triangle is a basic geometric form with three sides and three corners. Each side links to two adjacent sides, resulting in three corners where the sides meet. The angles within a triangle always sum to 180 degrees. Triangles are classified into three types: equilateral (all sides and angles are equal), isosceles (two sides and two angles are equal), and scalene (all sides and angles differ).

The properties of triangles in geometry are:

Angle Sum Property

Angle Sum Property is a fundamental property in geometry that asserts that the sum of all angles within a triangle is always 180 degrees. This technique is useful for solving for missing angles or determining triangle validity. For example, if two angles are 60 degrees each, the third angle must also be 60 degrees to meet this criterion.

Angle 1 + Angle 2 + Angle 3 = 180∘

angle_sum_property

Triangle Inequality Property

The total of any two sides of a triangle exceeds the length of the third side. In other words, the shortest path between two places is a straight line. This is expressed as:

a + b > c

Where a, b, and c are the lengths of the sides of the triangle.

Pythagoras Property

In a right triangle, the square of the hypotenuse's length (the side opposite the right angle) equals the sum of the squares of the other two sides. This is called the Pythagorean theorem.

__c_2 = __a_2 + __b_2

Hypotenuse length is denoted by c, whereas the other two sides' lengths are denoted by a and b.

Side Opposite the Greater Angle is the Longest Side

The side opposite the greatest angle in a triangle is the longest side. This is an observable property, not a formal theorem. When given a triangle's angles, it helps to determine which side is the longest.

Exterior Angle Property

Each exterior angle of a triangle equals the sum of its two remote interior angles. The mathematical expression is:

Exterior Angle = Sum of Remote Interior Angles

Congruence Property

Triangles of the same size and shape are said to be congruent. This attribute is useful in assessing if two triangles are identical. It may be proved by congruence criteria such as

These qualities are essential for understanding and solving triangle-related geometry issues.