Geometry-Polygons

Geometry-Polygons

15. Varions types of Quadrilaterals 
    (i)Trapezium             
    (ii) Isosceles Trapezium
    (iii) Parallelogram            
    (iv)Rhombus
    (v) Rectangle            
    (vi) Square             
    (vii) Kite

16. Trapezium: We have defined a trapezium as a quadrilateral having exacty one pair of parallel sides

(i)\( \left| \!{\underline {\, B \,}} \right. + \left| \!{\underline {\, C \,}} \right. = 180^0 \)  (ii)\( \left| \!{\underline {\, A \,}} \right. + D = 180^0 \)

17. Isosceles trapezium: A trapezium in which, non parallel sides are equal in length is called an isosceles trapezium.

(i)\( \left| \!{\underline {\, A \,}} \right. = \left| \!{\underline {\, B \,}} \right. \)  (ii)\( \left| \!{\underline {\, C \,}} \right. = \left| \!{\underline {\, D \,}} \right. \)

18.  Parallelogram

In a parallelogram, we have
    (i) the opposite sides are equal
    (ii) the opposite angles are equal 
    (iii) the diagonals bisect each other
Note:\( \left| \!{\underline {\, A \,}} \right. + \left| \!{\underline {\, B \,}} \right. = \left| \!{\underline {\, B \,}} \right. + \left| \!{\underline {\, C \,}} \right. = \left| \!{\underline {\, C \,}} \right. + \left| \!{\underline {\, D \,}} \right. = \left| \!{\underline {\, D \,}} \right. + \left| \!{\underline {\, A \,}} \right. = 180^0 \)

19.  Rhombus: Aparallelogram, having all sides equal, is called a rhombus.

Note: In a rhombus, diagonals are perpendicular bisectors of each other.

20. Rectangle: A parallelogram where each angle is a right angle, is called a rectangle.

Here, \( AB\parallel CD,BC\parallel AD \)
\( \left| \!{\underline {\, A \,}} \right. = \left| \!{\underline {\, B \,}} \right. = \left| \!{\underline {\, C \,}} \right. = \left| \!{\underline {\, D \,}} \right. = 90^0 \)   
21. Square: A square is a rectangle with a pair of equal adjacent sides
        
    Here, \( AB\parallel CD,BC\parallel AD \)
    \( AB = BC = CD = DA \) and \( \left| \!{\underline {\, A \,}} \right. = \left| \!{\underline {\, B \,}} \right. = \left| \!{\underline {\, C \,}} \right. = \left| \!{\underline {\, D \,}} \right. = 90^0 \)

22.  Kite: A quadrilateral is a kite, if it has two pairs of equal adjacent sides and unequal opposite sides
        
        Here, \( AB = AD,BC = CD \) but \( AB \ne BC,AD \ne CD \)
        
23. To construct a triangle, we require three measurements of sides or angles (atlest one of them is a side)

24.  A quadrilateral has 10 elements ( Four sides, four angles and two diagonals) and to draw a quadrilateral, any five independent elements must be given.