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Quadrilateral

Any 4-sided polygon is called a quadrilateral. It has four sides, four vertices and four angles.
A
In the adjoining figure, ABCD is a quadrilateral, where AB, BC, CD and DA are
its sides. A, B, C and D are the vertices and ∠A, ∠B, ∠C, and ∠D are the four
angles of the quadrilateral ABCD. D
∠A and ∠B, ∠B and ∠C, ∠C and ∠D, ∠D and ∠A are the adjacent angles and
∠A and ∠C, ∠B and ∠D are the opposite angles. B C

Quadrilaterals could be regular or irregular.

A D D Remember
A
Square is an example of regular quadrilateral
having four equal sides and rectangle is
an example of an irregular quadrilateral
having unequal sides but having the pairs
B C B C
of opposite equal sides.
Regular quadrilateral Irregular quadrilateral

An irregular quadrilateral can be a convex or concave quadrilateral.
Convex and Concave Quadrilateral

A quadrilateral in which both its diagonals lie in the interior and all its interior angles measure
less than 180° is called a convex quadrilateral.
A quadrilateral where one of the diagonals lies completely or partially in the exterior of the
quadrilateral and also at least one of its angles measuring greater than 180° is called a concave
quadrilateral.

A
D
A
Think and Answer
Is there any quadrilateral
possible in which both diagonals lie outside
C the boundary?
B C B D
Convex quadrilateral Concave quadrilateral
Angle Sum Property of Quadrilateral C

3 4
Let ABCD be a quadrilateral. Split it into two triangles by drawing a
diagonal AC. D

Clearly, ∠1 + ∠2 = ∠A ...(i)

And, ∠3 + ∠4 = ∠C ...(ii) 1
2
We know that the sum of the angles of a triangle is 180°. A B

Therefore, in ∆ABC, ∠2 + ∠4 + ∠B = 180° (Angle sum property of triangle) …(iii)
In ∆ACD, ∠1 + ∠3 + ∠D = 180° (Angle sum property of triangle) …(iv)

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