Ch 6.1 The Polygon Angle-Sum Theorems Objectives: a) To classify Polygons b) To find the sums of the measures of the interior & exterior s of Polygons.
Which of the following figures are polygons? yesNo
Special Polygons: Equilateral Polygon – Equilateral Polygon – All sides are . All sides are .
Special Polygons: Equiangular Polygon – Equiangular Polygon – All s are . All s are .
Special Polygons: Regular Polygon – Regular Polygon – Both Equilateral & Equiangular. Both Equilateral & Equiangular.
I. Classify Polygons by the number of sides it has. Sides nName Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon N-gon Interior Sum
How many degrees are in a triangle? We know this by the Triangle Angle- Sum Theorem
III. Polygon Interior sum A rectangle has how many sides? Without crossing lines, how many triangles can I make? Each triangle has 180 0, so if I have two triangles I have how many degrees?
III. Polygon Interior sum How many sides does this polygon have? Without crossing lines, how many triangles can I make? Each triangle has 180 0, so if I have three triangles I have how many degrees?
6 sides 4 Δs = 720 All interior sums are multiple of 180° Th(3-9) Polygon Angle – Sum Thm Sum of Interior # of sides S = (n -2) 180
Examples 2 & 3: Find the interior sum of a 15 – gon. Find the interior sum of a 15 – gon. S = (n – 2)180 S = (15 – 2)180 S = (13)180 S = 2340 Find the number of sides of a polygon if it has an sum of 900°. Find the number of sides of a polygon if it has an sum of 900°. S = (n – 2) = (n – 2)180 5 = n – 2 n = 7 sides
IV. Exterior s of a polygon
Th(3-10) Polygon Exterior -Sum Thm The sum of the measures of the exterior s of a polygon is 360°. The sum of the measures of the exterior s of a polygon is 360°. Only one exterior per vertex. Only one exterior per vertex m 1 + m 2 + m 3 + m 4 + m 5 = 360 For Regular Polygons = measure of one exterior The interior & the exterior are Supplementary. Int + Ext = 180
Example 4: How many sides does a polygon have if it has an exterior measure of 36°. How many sides does a polygon have if it has an exterior measure of 36°. = = 36n 10 = n
Example 5: Find the sum of the interior s of a polygon if it has one exterior measure of 24. Find the sum of the interior s of a polygon if it has one exterior measure of 24. = 24 n = 15 S = (n - 2)180 = (15 – 2)180 = (13)180 = 2340
Example 6: Solve for x in the following example. Solve for x in the following example. x sides Total sum of interior s = x = x = 360 x = 80
Example 7: Find the measure of one interior of a regular hexagon. Find the measure of one interior of a regular hexagon. S = (n – 2)180 = (6 – 2)180 = (6 – 2)180 = (4)180 = (4)180 = 720 = 720 = 120