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.