# Properties of Triangle

Properties of Triangle A triangle has 6(Six) elements consisting of

3 (three) sides and 3 (three) angles. These

6 (six) elements constitute the following properties of a Triangle mentioned as under: 1) The sum of any two sides of a triangle is always greater than the third the side.

In ABC, we have, AB + BC > AC, AC + AB > BC and AC + BC > AB

2)  The difference between any two sides of a triangle is less than the third side.

In ABC, we have, AB – BC < AC, AC – AB < BC, AC – BC < AB, etc

3) The sum of three angles of triangle is always 180°.

In ABC, we have, ABC + ACB + BAC = 180°

This property is also known as Angle Sum Property of a Triangle.

4) Exterior Angle of a Triangle is equal to the sum of Interior Opposite Angles.

In ABC, we have, Ext. ACD = ABC + BAC

### What are the properties of triangle

Let us prove that the sum of three angles of triangle is always 180°. In order to prove that the sum of three angles of triangle is always 180°, let us consider a

ABC and through the vertex A of it, let a line PQ is drawn parallel to BC. (PQ∥BC)

From the figure we have, Let us prove that Exterior Angle of a Triangle is equal to the sum of Interior Opposite Angles. In order to prove that, Exterior Angle of a Triangle is equal to the sum of Interior Opposite Angles,

let us extend BC to a point D. Then according to Linear Pair Axiom, we must have #### Properties of Rational Numbers

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