Quadrilaterals

✤ Quadrilateral - A four sided closed polygon is called a quadrilateral

 Properties :-

(i) It has 4 sides (AB, BC, CD, AD)

(ii) It has 4 angles (∠A, ∠B, ∠C and ∠D).

(iii) It has 4 vertices (A, B, C, D)

(iv) It has 2 diagonals (AC, BD)

(v) A diagonal of a quadrilateral.

(vi) Sum of angles in a quadrilateral is 360° (∠A + ∠B + ∠C + ∠D = 360°).

Types of Quadrilateral

(i) Parallelogram: In a quadrilateral if two pairs of opposite sides are parallel, then it is

      called a parallelogram.

       (Or)

  If one pair of opposite sides is parallel and equal, then it is called a parallelogram.

  Properties:

(i) Opposite sides are equal (AB = CD, BC = BD)

(ii) Opposite angles are equal (∠B = ∠D, ∠A = ∠C)

(iii) Diagonals bisect each other (AC = BD).

(iv) A diagonal of a parallelogram divides it into two equal parts (ar ΔABC) = ar (ΔACD)

(ii) Rectangle: A parallelogram in which each angle is 90° is called a rectangle.

  Properties:

(i) Opposite sides are equal

(ii) All the angles are equal (each 90°)

(iii) Diagonals bisects each other.

(iv) A diagonal of a rectangle divides into two equal parts (congruent

  triangles).

(v) Diagonals are equal.

(iii) Rhombus - A parallelogram in which all the sides are equal is called a rhombus

    Properties :

(i) All the sides are equal.

(ii) Diagonals bisect each other at right angles.

(iii) A diagonal of a rhombus divides into two equal parts.

(iv) Square - A rhombus in which each angle is 90° is called a square.

   Properties:

(i) All the sides are equal.

(ii) All the angles are equal.

(iii) Diagonals are equal.

(iv) Diagonals bisect each other at 90°.