POLYGONS : POLYGONS The word ‘ poly gon ’ is a Greek word. Poly means many and gon means angles.
PowerPoint Presentation : Definition of Polygon : A Polygon is any closed shape which has three or more sides . Polygon Types : (a) Regular Polygons All their sides are the same length , and all their angles are the same size e.g. squares, equilateral triangles …. (b) Irregular Polygons They do not have equal length sides and angles Rectangle, kites and trapeziums are an irregular polygons, but so too are shapes like this:
Examples of Polygons : Examples of Polygons
These are not Polygons : These are not Polygons
PowerPoint Presentation : 1. Triangles There are 4 types of triangles you need to be on the look-out for and you must know the properties of (what is special about) each of them Equilateral Isosceles Right Angled Scalene All angles are equal (60 0 each) All sides are the same length Two angles are equal Two sides are the same length One angle is 90 0 All sides may be different lengths All angles may be different All angles are different sizes All sides are different lengths
PowerPoint Presentation : 2. Quadrilaterals A Quadrilateral is any four-sided shape. There are lots of quadrilaterals flying around, and it is important that you know the properties of each… so here they are! Square Parallelogram All angles are right-angles (90 0 each) All sides are the same length Two pairs of parallel lines Opposite angles are equal Opposite sides are the same length Two pairs of parallel side Rectangle All angles are right-angles (90 0 each) Opposite sides are the same length Opposite sides are parallel
PowerPoint Presentation : Rhombus Opposite angles are equal All sides are the same length Opposite sides are parallel Notice: Each of the four shapes above are very similar… in fact, they are all just special types of parallelograms ! See how they each have two pairs of parallel sides … and then it just certain other properties that make them different shapes! Trapezium All angles may be different sizes All sides may be different lengths Opposite sides are parallel Kite One pair of equal angles Adjacent sides are the same length No pairs of parallel sides
PowerPoint Presentation : 3. Other Polygons As soon as you get above 4 sides, the names of the polygons start to get a bit weird. Here are some of the main ones you should learn. Notice: Each of the shapes below are regular polygons as all the sides and angles are the same. Pentagon Hexagon Heptagon / Heptagon Octagon Nonagon Decagon Dodecagon Icosagon 5 sides 6 sides 7 sides 8 sides 9 sides 10 sides 12 sides 20 sides
POLYGON Terminology : POLYGON Terminology Side: One of the line segments that make up a polygon. Vertex: Point where two sides meet.
PowerPoint Presentation : Vertex Side
PowerPoint Presentation : Interior angle : An angle formed by two adjacent sides inside the polygon. Exterior angle : An angle formed by two adjacent sides outside the polygon. ANGLES OF POLYGON
PowerPoint Presentation : Interior angle Exterior angle
Let us revise : Let us revise Interior angle Diagonal Vertex Side Exterior angle Polygons
PowerPoint Presentation : An exterior angle of a regular polygon is formed by extending one side of the polygon. Angle CDY is an exterior angle to angle CDE Exterior Angle + Interior Angle of a regular polygon =180 0 D E Y B C A F 1 2
PowerPoint Presentation : 120 0 120 0 120 0 60 0 60 0 60 0
PowerPoint Presentation : No matter what type of polygon we have, the sum of the exterior angles is ALWAYS equal to 360º. Sum of exterior angles = 360º
PowerPoint Presentation : In a regular polygon with ‘n’ sides Sum of interior angles = (n -2) x 180 0 WHY THE ABOVE FORMULA? Well, it’s all to do with triangles… We know that the sum of the interior angles of any triangle is 180 0 , right? Well… we can split any polygon up into triangles , like this… And there will always be 2 fewer triangles than there are sides! 6 sides 4 triangles 1 2 3 4 Interior Angles of Polygons For Regular Polygons Because all angles are equal in regular polygons , you can work out the size of each interior angle like this: Size of each interior angle = Sum of all interior angles ÷ Number of sides
PowerPoint Presentation : Exterior Angles of Polygons An exterior angle is an angle outside the polygon made by extending one of the sides… Sum of all exterior angles = 360 0 Why? Well, if you keep moving around the polygon , extending the sides and measuring each exterior angle, by the time you get back to where you started you have made… a circle ! Which, as we all know, contains 360 0 For Regular Polygons If all interior angles are equal for regular polygons, then all exterior angles are equal too, so to work out the size of each one, we do this… Size of each exterior angle = 360 0 ÷ Number of sides exterior angle Note : If you know the sizes of the exterior angles of a regular polygon, then you can also work out the sizes of the interiors by remembering that angles on a straight line add up to 180 0 Size of each interior angle = 180 0 – Size of each exterior angle
Let us explore some problems : Let us explore some problems Find the measure of each interior angle of a polygon with 9 sides. Ans : Find the measure of each exterior angle of a regular decagon. Ans : How many sides are there in a regular polygon if each interior angle measures 165 0 ? Ans : Is it possible to have a regular polygon with an exterior angle equal to 40 0 ? Ans :
Let us explore some problems : Let us explore some problems Find the measure of each interior angle of a polygon with 9 sides. Ans : 140 0 Find the measure of each exterior angle of a regular decagon. Ans : 36 0 How many sides are there in a regular polygon if each interior angle measures 165 0 ? Ans : 24 sides Is it possible to have a regular polygon with an exterior angle equal to 40 0 ? Ans : Yes
Polyhedra : Polyhedra If all the faces of a solid are polygons, then that solid is called a polyhedron . Note : The polyhedra can be named by their numbers of faces.