In the given triangle, Exterior angle (e) = ∠a + ∠b Thus, the side AC is the longest side.Īs per the exterior angle theorem, the exterior angle of a triangle is always equal to the sum of the interior opposite angles. In this triangle, ∠B is the greatest angle. ![]() In order to understand this property which says that the side opposite the greater angle is the longest side, observe the triangle given below. Side Opposite the Greater Angle is the Longest Side Observe the figure given below to see the altitude, the base, and the hypotenuse. Mathematically, it can be expressed as Hypotenuse² = Base² + Altitude². If a = 4 units, b = 6 units, c = 3 units, let us verify the triangle inequality property as follows:Īs per the Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the figure given above which shows △ABC which represents the Triangle inequality property. ![]() In the given triangle, ∠P + ∠Q + ∠R = 180° Triangle Inequality PropertyĪs per the triangle inequality theorem, the sum of the length of the two sides of a triangle is greater than the third side. Angle Sum PropertyĪs per the angle sum property, the sum of the three interior angles of a triangle is always 180°. Some of the important properties of a triangle are listed below. ![]() The properties of a triangle help us to identify relationships between different sides and angles of a triangle.
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