Basics of Geometry POLYGONS
POLYGONS A polygon is a closed figure formed by three or more line segments, called sides. > Each side is joined to two other sides at its endpoints and the endpoints are called vertices. Triangle (3 sides) Pentagon Quadrilaterail(5 sides) (4 sides) The simplest polygon is a triangle which has three sides.
POLYGONS > A quadrilateral can be divided into two triangles and a pentagon can be divided into three triangles as shown in the figure. > Similarly, if a polygon has n sides, it can be divided into (n-2) triangles -If there is a polygon of 5 sides, then the number of triangles it can be divided into are (5-2), that is 3 triangles
POLYGONS The sum of the measures of the interior angles of a triangle is 180 degrees > The sum of measures of the interior angles of an n-sided polygon is (n-2)(180) degrees. For example, the sum for a quadrilateral (n-4) is (4-2)(180)= 360 degrees and the sum for a hexagon (n 6) is (6-2)(180) 720 degrees 120 120 120 120 120 120
POLYGONS > A polygon in which all sides are congruent and all interior angles are congruent is called a regular polygon For example, in regular octagon (which has 8 sides), the sum of the measures of the interion angles is (8-2) (180)-1,080 degrees. Therefore, the measure of each angle is 1080/8= 135 degrees. Regular Polygons 120 120 135 135 60 135* 135 120 120 60 135 135 20 120 135 135 0
PROBLEM 1 ) Quantity A The length of a side of a regular hexagon with a perimeter of 19.5 Quantity B The length of a side of regular octagon with a perimeter of 26 a) b) c The two quantities are equal d) Quantity A is greater Quantity B is greater The relationship cannot be determined from the information given
19.S 3.25 6 6 2-25
For the pentageon shoon above, y- 8o Iog A) Quantity A is areatr uantity B is areatest C) The tuwo quantites are D) The velatriorship canot be deteuninad from the inloumetion iven.
Sol) 30 cSun ol interfor ang (n-2)180 (s-2 12o les 210 eo, Quantty A Quartitye
20 (G-2)180 (890 o 4t 6-2)180-720 ,20 20 9oo but its not merto ulau o not