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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