1. Geometry
6.1 Polygons

2. Goals: Identify polygons & describe them.
Determine the measure of angles in a quadrilateral.
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Geometry 6.1 Polygons

3. Polygon A plane figure made of three or more segments (sides).
Each side intersects exactly two other sides at their endpoints.
Polygons are named by vertices in consecutive order, going CW.
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Geometry 6.1 Polygons

4. Examples
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Geometry 6.1 Polygons

5. Sides don’t intersect at endpoints.
These are NOT polygons.
Figure not closed.
No Sides or Segments
Sides don’t intersect at endpoints.
November 9, 2018
Geometry 6.1 Polygons

6. Naming Polygons
The name tells you how many sides and how many vertices the polygon has.
Learn the names: memorize!
Be able to spell them.
November 9, 2018
Geometry 6.1 Polygons

7. Triangle – 3 sides C Name: ABC A B November 9, 2018
Geometry 6.1 Polygons

8. Quadrilateral – 4 sides Q T R S Name: QRST November 9, 2018
Geometry 6.1 Polygons

9. Pentagon – 5 sides N Name: JKLMN M J K L November 9, 2018
Geometry 6.1 Polygons

10. Hexagon – 6 sides C B A D E F Name: FEDCBA November 9, 2018
Geometry 6.1 Polygons

11. Heptagon – 7 sides
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Geometry 6.1 Polygons

12. Octagon – 8 sides
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Geometry 6.1 Polygons

13. Nonagon – 9 sides
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Geometry 6.1 Polygons

14. Decagon – 10 sides
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Geometry 6.1 Polygons

15. More than 10 sides: n-gon 14-gon has 14 sides. 200-gon has 200 sides.
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Geometry 6.1 Polygons

16. Diagonals A segment that joins two non-consecutive vertices.
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Geometry 6.1 Polygons

17. Convex & Concave All polygons are either convex or concave.
It’s easy to determine which category falls in just by looking.
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Geometry 6.1 Polygons

18. Convex All diagonals are in the interior of the polygon.
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Geometry 6.1 Polygons

19. Concave Think: Caved In
At least one diagonal (or part of one) is in the exterior of the polygon.
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Geometry 6.1 Polygons

20. Equilateral Polygons All sides are congruent. November 9, 2018
Geometry 6.1 Polygons

21. Equiangular Polygons All the angles have the same measure.
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Geometry 6.1 Polygons

22. REGULAR Polygons Are equilateral AND equiangular. November 9, 2018
Geometry 6.1 Polygons

23. Theorem 6.1 The sum of the angles of a quadrilateral is 360. 4 1 2 3
1 + 2 + 3 + 4 = 360
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Geometry 6.1 Polygons

24. Proof B + 1 + 3 = 180 D + 2 + 4 = 180A B C D 3 4 1 2
B + 1 + 3 = 180
D + 2 + 4 = 180
B + D + (1 + 2) + (3 + 4) = 360
But 1 + 2 = A and 3 + 4 = C
B + D + A + C = 360
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Geometry 6.1 Polygons

25. Example Solve for x. x 55 55 x + x + 55 + 55 = 360 2x + 110 = 360
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Geometry 6.1 Polygons

26. Your Turn Find the measure of each angle. A D B C (5x + 10)
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Geometry 6.1 Polygons

27. Solution 80 132 82 66 A D B C (5x + 10) (4x + 10) (3x + 40)
(5x + 10) + (8x + 20) + (3x + 40) + (4x + 10) = 360
20x + 80 = 360
20x = 280
x = 14
November 9, 2018
Geometry 6.1 Polygons