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Unit 3 Foundations of Geometry Review

Unit 3 Foundations of Geometry Review. Oct 8, 2012. Names of Polygons. You need to know how many sides there are for the different polygons Square – 4 pentagon - 5 Triangle – 3 nonagon - 9 Hexagon – 6 octagon – 8 Heptagon – 7 Decagon – 10

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Unit 3 Foundations of Geometry Review

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  1. Unit 3 Foundations of Geometry Review Oct 8, 2012

  2. Names of Polygons You need to know how many sides there are for the different polygons Square – 4 pentagon - 5 Triangle – 3 nonagon - 9 Hexagon – 6 octagon – 8 Heptagon – 7 Decagon – 10 Dodecagon - 12

  3. Other Vocabulary Polygon – a shape cannot be a polygon if it has a curve Regular – all sides and angles are congruent (the shape must be marked with both – do not assume)

  4. Other Vocabulary Equiangular – all angles are equal Concave – there is at least one chunk carved into the polygon n = the number of sides in the polygon

  5. Quick Cheat Sheet for formulas Sum of interior angles (n – 2) 180 Sum of exterior angles for ANY polygon 360 Each or An interior angle(n—2)180 n Each or An exterior angle360 n

  6. Instructions Be sure and READ the directions so you know …….. What you have and what you need to find. Write the formulas on the top of your test as soon as you get your test. Be sure you know how to use the formulas.

  7. Examples 1. Find the sum of the measures for each regular polygon. A. Nonagon …9 sides (9-2)180 ….. 7 x 180 = 1260° • 14-gon …..14 sides (14-2)180 12 x 180 = 2160°

  8. Examples • Find the measure of the missing angle. 50 72 105 X Ok, you know this is a rectangle and it has 4 sides. How much should all of the angles add to? 360 So you set up an equations where 50 + 72 + 105 + X = 360. Combine like terms and you get 227 + x = 360 Subtract 227 from both sides and your missing angle measure is 133°

  9. Another example Find the measure of the missing angle in a regular 15-gon. OK you know a 15-gon has 15 sides, right? Use the formula to find the total of the interior angles….. (15-2)180 or 13 x 180 = 2340° You know “regular” means all the angles are congruent so divide 2340 by 15 and each angle measure is 156°

  10. Example Find the measure of an exterior angle for each polygon. Formula???? 360 n 1. Decagon 360 10 = 36°

  11. Examples Find the measure of an exterior angle for each polygon. 2. Heptagon 360 7 = 51.42, round to 51.4°

  12. Examples Find the measure of an interior angle. Formula? (n—2)180 n 1. Regular Pentagon 5 sides…. (5—2)180 5

  13. (5—2)180 5 3 x 180 = 540 5 = 108°

  14. Examples An interior angle measure of a regular polygon is given. Find the number of sides of the polygon. 1. 120° OK set it up as 120 = (n-2)180 n and solve First multiply both sides by n to get 120n = (n-2)180 Then distribute the n on the right side 120n= 180n-360 Next subtract 180 from both sides 180 – 120 is –60 Now you have --60n = --360 --60 --60 Divide both by negative 60 to get 6. If you do it in the computer it will say negative but a negative divided by a negative is POSITIVE

  15. Let’s do another An interior angle measure of a regular polygon is given. Find the number of sides of the polygon. 155° Formula? 155=(n—2)180 n Step 1 multiply both sides by n ….. 155n = (n-2)180 Step 2 subtract 180 from both sides…. –25n = (n-2)180 Step 3 distribute the 180…. --25n = 180n—360 Step 4 Subtract 180 from both sides…. --205n = --360 Step 5 Divide both sides by –205….. 1.44 and round to 1.4

  16. More Examples An exterior angle of a regular polygon is given. Find the number of sides in the polygon. Formula?? Remember all exterior angles add up to 360 1. 120° 360 120 = 3 sides • 36° 360 36 = 10 sides

  17. Add some algebra in…… 5x + 1 6x-2 3x + 3 2x To find any of these angle measures you have to solve for x first. This is a 4 sided shape so the total of the angle measures is…….. 360 (4—2) 180 = 360 Now you add up all of the measures to equal 360. Combine like terms and solve algebraically….answer on next slide……

  18. Using Algebra, cont’d 6x + 2 + 5x + 1 + 3x + 3 +2x = 16x + 5 = 360 -5 -5 16x = 355 • 16……. X = 22.19 To find each angle you have to plug 22.19 in for each X and solve 6(22.19) —2 = 131.14

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