Download presentation

Presentation is loading. Please wait.

Published byRosanna McLaughlin Modified over 6 years ago

1
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.

2
Which of the following figures are polygons? yesNo

3
Special Polygons: Equilateral Polygon – Equilateral Polygon – All sides are . All sides are .

4
Special Polygons: Equiangular Polygon – Equiangular Polygon – All s are . All s are .

5
Special Polygons: Regular Polygon – Regular Polygon – Both Equilateral & Equiangular. Both Equilateral & Equiangular.

6
I. Classify Polygons by the number of sides it has. Sides 3 4 5 6 7 8 9 10 12 nName Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon N-gon Interior Sum

7
How many degrees are in a triangle? We know this by the Triangle Angle- Sum Theorem

8
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?

9
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?

10
6 sides 4 Δs 4 180 = 720 All interior sums are multiple of 180° Th(3-9) Polygon Angle – Sum Thm Sum of Interior # of sides S = (n -2) 180

11
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)180 900 = (n – 2)180 5 = n – 2 n = 7 sides

12
IV. Exterior s of a polygon. 1 23 1 2 3 45

13
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. 1 2 3 4 5 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

14
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°. = 36 360 = 36n 10 = n

15
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

16
Example 6: Solve for x in the following example. Solve for x in the following example. x 100 4 sides Total sum of interior s = 360 90 + 90 + 100 + x = 360 280 + x = 360 x = 80

17
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

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google