**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

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