What is the Angle Sum Property of a Quadrilateral?
This property states that the sum of all angles of a quadrilateral is 360°. Let’s prove this.
Theorem: Sum of all four angles of a quadrilateral is 360°.
Angle Sum Property of a Quadrilateral Proof
Let ABCD be a quadrilateral.
Join AC.
Now notice,
∠1 + ∠2 = ∠A
∠3 + ∠4 = ∠C
Therefore, from triangle ABC
∠4 + ∠2 + ∠B = 180o
Similarly, from triangle ADC
∠3 + ∠1 + ∠D = 180o
Adding these two equations,
∠4 + ∠2 + ∠B + ∠3 + ∠1 + ∠D = 360o
(∠1 + ∠2) + (∠3+ ∠4) + ∠B + ∠D = 360o
∠A + ∠C + ∠B + ∠D = 360o
Thus, this proves that sum of all interior angles of a quadrilateral is 360°.
Angle Sum Property of a Quadrilateral
Angle Sum Property of a Quadrilateral: Quadrilaterals are encountered everywhere in life, every square rectangle, any shape with four sides is a quadrilateral. We know, three non-collinear points make a triangle. Similarly, four non-collinear points take up a shape that is called a quadrilateral. It has four sides, four angles, and four vertices.
Both the figures above are examples of quadrilaterals. ABCD is a quadrilateral. AB, BC, CD, and DA are the four sides of the quadrilateral. A, B, C, and D are four vertices, and ∠A, ∠B, ∠C, and ∠D are the angles of this quadrilateral. Before coming to the Angle Sum Property of Quadrilateral we have to know some basic terminologies of quadrilateral, which are discussed below in the article.
Table of Content
- About Angle Sum Property of a Quadrilateral
- What is the Angle Sum Property of a Quadrilateral?
- Theorem: Sum of all four angles of a quadrilateral is 360°.
- Angle Sum Property of a Quadrilateral Proof
- Quadrilateral Angles
- Do Sum of Opposite Angles in a Quadrilateral equal 180 Degrees?
- Types of Quadrilaterals
- Solved Examples on Angle Sum Property of Quadrilateral
- Angle Sum Property of a Quadrilateral Worksheet
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