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Example: Sum of Four Sides of a Quadrilateral is Less than Twice the Sum of its Diagonals?

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Explanation:

 

 

Quadrilateral

 

Quadrilateral


Six different types of quadrilaterals

Edges and Vertices

4

Internal angles (degrees)

90° (for square)

 

 

In Euclidean plane geometry, a quadrilateral is a polygon with four sides (or 'edges') and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on. The word quadrilateral is made of the words quad (meaning "four") and lateral (meaning "of sides").The interior angles of a simple quadrilateral add up to 360 degrees of arc

 

http://en.wikipedia.org/wiki/Quadrilateral

 

The sum of the lengths of any two sides of a triangle always exceeds the length of the third side, a principle known as the triangle inequality. (Our solved example in mathguru.com uses this concept)

Since the vertices of a triangle are assumed to be non-collinear, it is not possible for the sum of the length of two sides be equal to the length of the third side.

 

http://en.wikipedia.org/wiki/Triangle

 

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.