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 to 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,
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,
Step 3:
Step 4:
Step 5: Substituting
We have thus proved the angle sum property of a triangle.
Video Lesson on Angle Sum Property of Triangle
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