What is a Quadrilateral? What are Adjacent sides, Opposite sides, Adjacent Angles and Opposite angles of a Quadrilateral?

The word ‘quad’ means four and the word ‘lateral’ means sides.
A quadrilateral is a plane figure bounded by four line segments(sides) and four angles.

ABCD is a quadrilateral. The points A, B, C, D are its vertices. The line segments AB, BC, CD, DA are four sides and $\angle A ,\angle B ,\angle C,\angle D$ are four angles of quad. ABCD.

Consecutive or Adjacent Sides 

If two sides have a common end-point(vertex), they are called Consecutive or adjacent sides. AB & BC; BC & CD; CD & DA; DA & AB are four pairs of adjacent sides.

Opposite Sides 

If two sides have no common end-point(vertex), they are called opposite sides. AB & CD; AD & BC are two pairs of opposite sides.

Adjacent Angles 

If two angles have a common arm between them, they are adjacent angles.
$\angle A\And \angle B,\angle B\And \angle C,\angle C\And \angle D,\angle D\And \angle A$ are four pairs of the adjacent angles.

Opposite Angles 

If two angles don’t have a common arm, they are opposite angles. $\angle A\And \angle C,\angle B\And \angle D$ are two pairs of opposite angles.

 Note:

  • The sum of the four angles of a quadrilateral is ${{360}^{{}^\circ }}$.
  • If the sides of a quadrilateral is produced in order, the sum of the four exterior angles so formed is ${{360}^{{}^\circ }}$. 
  • Area of quadrilateral ABCD = $\frac{1}{2}$ (Length of a diagonal) $\times $ (sum of the lengths   of perpendiculars from the remaining two vertices on it)
              = $\frac{1}{2}\times BD\times ({{h}_{1}}+{{h}_{2}})$

   
    Click Home for more Mensuration: Properties and formulas

No comments:

Post a Comment