**Triangle**:

In geometry, triangle is one of the basic shapes. **Triangle is the smallest polygon**. It consists of three edges and three vertices. A triangle with vertices P, Q and R is denoted as ∆PQR. In a triangle, three sides and three angles are referred as the elements of the triangle. Angle sum property and exterior angle property are the two important attributes of a triangle. What is angle sum property of a triangle? How to prove angle sum property? It is discussed here on.

A triangle consists of interior and exterior angles. **Interior angle** is defined as the angle formed between two adjacent sides of a triangle. **Exterior angle** is defined as the angle formed between a side of triangle and an adjacent side extending outward.For ∆ABC, Angle sum property of triangle declares that

*Sum of all the interior angles of the triangle is 180 °. *

That is,

\(m\angle{A}~+~m\angle{B}~+~m\angle{C}\)

**Proof of Angle Sum Property Theorem **

These are the following steps involved to prove angle sum property theorem:

Step 1: Draw a line AB through the vertex P and parallel to the side QR of a triangle PQR.

Step 2: Now, \(\angle{APQ}~+~\angle{QPR}~+~\angle{RPB}\)

Step 3:\(\angle{APQ}\)

Step 4: \(\angle{RPB}\)

Step 5: Substituting \(∠APQ\)

We have thus proved angle sum property of a triangle. For the complete understanding of the topic please visit www.byjus.com or download the Byju’s – The Learning App.

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