
Quadrilaterals,
Polygons  Regular Polygons 


Cyclic quadrilateral 
Tangential quadrilateral

Polygons

Regular
polygons 





Cyclic quadrilateral 
A
quadrilateral inscribed in a circle, so that all its vertices
lie on the circumference is called a cyclic
quadrilateral. 
The
opposite angles of a cyclic quadrilateral are supplementary. 


a
+ g = b + d = 180°, 
d_{1
}· d_{2}
= a_{ }· c + b _{
}· d 
perimeter
P
= a + b
+ c
+ d, s
= 1/2P 
area 





Tangential quadrilateral

A
quadrilateral whose sides all lie tangent to the circle
inscribed within the quadrilateral is called a tangential
quadrilateral. 


s
= a +
c = b + d, 
perimeter
P
= a + b
+ c
+ d, s
= 1/2P 

area 
A
= r · s 




Polygons

A
polygon is closed plane figure
bounded by a number of straight line segments with the same
number of vertices. 
The
sum of interior angles is (n

2) · 180°, where n
is the number of sides of a polygon. 
The
sum of exterior angles of a polygon is 360°. 


d_{n
} number
of diagonals 
b^{'}_{
} the
exterior angle 
d_{n
}= 1/2 · n · (n


3) 

S_{n}=
(n

2)
· 180° 
 the
sum of interior angles 



Regular
polygons 
In
a regular polygon all sides are equal and all its angles are
equal. 
The
exterior angle of a regular polygon is b^{'
}= 360°/n, where n
is the number of sides of a regular polygon. . 


a
=
b^{'}
= 360°/n

b^{'}_{
} the
exterior angle 
b
=
180°

b^{'}
= (n

2)
· 180°/n, 
P = n · a 
d_{n
}= 1/2 · n · (n


3) 
 number
of diagonals 
A
= 1/2 · n · a · r
= 1/2P · r 

area of a regular polygon 










Beginning
Algebra Contents D 



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