Angle Properties and Circle Theorem

Notes on Angle Properties and Circle Theorem

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  • Created on: 25-09-12 17:47
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IGCSEMATHSGEOMETRY
Angle Properties and Circle Theorems
Line, Ray, Line Segment (Review):
Line: It does not have a definite length or an end point and can be extended in both directions. It is
represented by the symbol. Line AB is written as AB . It cannot be measured.
Ray : It does not have a definite length and has only one end point. It can be extended in one direction
only. It has a definite length. It is represented by the symbol . Ray AB is written as AB . It cannot be
measured.
Line Segment: It has two end points. None of the ends can be extended.
It is represented by the symbol
--.Line segment AB is written as AB . It can be measured.
Angle Properties of Regular Polygons:
A polygon is usually described as a closed two- dimensional shape bounded by straight lines. Examples
of polygon include triangles, pentagons, quadrilaterals etc.
A regular polygon has sides of equal length and all its angles are of equal size.
E.g. Square, Rectangle, Triangle etc.
The name of each polygon is derived from the number of angle it contains. The following list identifies
some of these polygons.
3 angles= triangle, 4 angles= tetragon, 5 angles= pentagon, 6 angles= hexagon, 7 angles= heptagon,
8 angles= octagon, 9 angles= nonagon, 10 angles= decagon, 12 angles= dodecagon.
The sum of interior angles of a polygon: A
A B E B
C D D C
From the vertex A of the following polygons, a line has been drawn to all other vertexes.
As you can see, the number of triangles is always two less than the number of sides.
There will be (n-2) triangles.
1 | PageIGCSE2012

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IGCSEMATHSGEOMETRY
Since the angles of a triangle add up to 180°, the sum of the interior angles of a polygon will be 180(n-2)
degrees.
Example: The trapezium has 4 sides.
180(4-2)= 180(2)=360°
The Sum of exterior angles of a polygon:
a b Angles a, b, c, d, e are the exterior angles of the polygon on the left.…read more

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IGCSEMATHSGEOMETRY
Angle between Tangent and Radius:
The angle between tangent of a point and the radius to the same point
on the circle forms a right angle (which is 90°)
Angle properties of Irregular polygons:
To find the angle of an irregular polygon, you have to keep in mind that the sum of interior angles of a
polygon is found by using the formula 180(n-2) and the sum of all the exterior angles of any polygon is
always 360°.…read more

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IGCSEMATHSGEOMETRY
If the angle at the center is 2x, then each of the angles at the circumference must be equal to x°
Angles in opposite segments:
A
B
4 | PageIGCSE2012…read more

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