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Lets be G!

Title art by myselfA compendium ofgeometry andpolygons

By Ariana Lotfi* In the title, G means geometrical

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Table of Contents1. Regular Polygons

2. The Sum of Angles in a Polygon

3. The Exterior Angles of a Polygon

4. Area of Composed Shapes

5. Parallel Lines

6. Perpendicular Lines

7. Bisector of an Angle

8. Square

9. Rectangle

10. Parallelogram

11. Kite

12. Trapezoid

13. Rhombus

14. Pentagon

15. Hexagon

16. Heptagon

17. Octagon

18. Nonagon

19. Decagon

20. Undecagon

21. Dodecagon

22. Reflection

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Regular Polygons

Do you think a circle is a polygon? Why?No. I dont think a circle is a polygon. A circle is acircle; its completely round. A polygon is defined as a

closed plane figure bounded by straight sides, having at

least three distinct sides and angles between them. But intheory, some people might think a circle is a polygon.

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Sum of angles in aPolygon

What are two different methods to find a sum ofangles in any polygon?They are as listed:

A: Multiply 180 degrees by the number of sides a polygonhas and then divide it by 360 degrees.EX/ (180 n) 360

B:Subtract the sides of the polygon by two and thenmultiply it by 180 degrees.

EX/ 180(n 2).

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Exterior Angles ofPolygons

What would be the sum of all exterior angles in aquadrilateral?The sum of all exterior angles in a quadrilateral would be

360 degrees. It would be 360 degrees because if you put

them all together they form the angle all the way around apoint.

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Area of Triangle, Rectangle,Parallelogram, and Trapezoid

How to find the area of composed shapes?Triangle: To find the area of a triangle, multiply thebase by the height, and then divide by 2.Formula: Area = b hRectangle: To find the area of a rectangle, you multiplythe base by the height.Formula: Area = b hParallelogram: To find the area of a parallelogram youmultiply the base by the height.

Formula: Area = b hTrapezoid: To find the area of a trapezoid, you take thesum of its bases, multiply the sum by the height of thetrapezoid, and then divide the result by 2.

Formula:

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Parallel Lines

What problems would there be in your picture if thelines were not parallel?There would be problems with the architecture. It would be

difficult for the structure to hold the weight of thebuilding if the pillars were not parallel. Another reason

would be that it would lookbad and it wouldnt make senseif the length and the base were the same length.

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Perpendicular Lines

What would happen if the lines on your picture werenot perpendicular?Well, for one, it would be extremely difficult towalk down the stairs if they werent perpendicularand they were actually slanted. People would befalling and hurt themselves ... a lot. It would ALSOlook bad, just like in the parallel lines.

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Bisector of anangle

In what quadrilaterals do diagonals bisect eachother?

Squares, rectangles, rhombuses, kites, andparallelograms.

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Square

A four-sided polygon.

1.Its a quadrilateral

2.All four sides are equal3.Has two pairs of parallel sides4.All four angles are equal (90 degrees)5.Diagonals are equal6.Diagonals are perpendicular7.Diagonals bisect each other8.Has four lines of symmetry

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Rectangle

A four-sided polygon.1.Its a quadrilateral2.Has two pairs of equal sides3.Has two pairs of parallel sides4.All four angles are equal (90 degrees)5.The diagonals are equal6.The diagonals are NOT perpendicular (not 90degrees)7.Diagonals bisect each other8.Has two lines of symmetry

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Kite

A four-sided polygon.1.Its a quadrilateral2.Has two pairs of equal sides3.Has no parallel sides4.Has two pairs of parallel angles5.Diagonals are not equal6.Diagonals are perpendicular7.One diagonal bisects but the other doesnt8.Has two lines of symmetry

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Trapezoid(Isosceles)

A four-sided polygon.1.Its a quadrilateral2.Has two pairs of equal sides3.

Has only one pair of parallel sides

4.Has two pairs of equal angles5.Diagonals are equal6.Diagonals are not perpendicular7.Diagonals dont bisect each other8.One line of symmetry

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Rhombus

A four-sided polygon.1.Its a quadrilateral2.All four sides are equal3.Has two pairs of parallel sides4.

Has two pairs of equal angles

5.Diagonals are not equal6.Diagonals are perpendicular (make 90 degreeangles)7.Diagonals bisect each other8.Has two lines of symmetry

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Pentagon

1.Has five sides2.Has five diagonals3.Has three triangles4.The sum of all the interior angles equals 540degrees5.The interior angle of a regular pentagon is 108degrees6.The exterior angle of a regular pentagon is 72degrees

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Hexagon

1.Has six sides2.Has nine diagonals3.Has four triangles4.The sum of all interior angles equal 720 degrees5.The interior angle of a regular hexagon is 120degrees6.The exterior angle of a regular hexagon is 60degrees

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Heptagon

1. Has seven sides2. Has fourteen diagonals3. Has five triangles4. The sum of all interior angles equal 900degrees5. The interior angle of a regular heptagon isabout 128.5 degrees6. The exterior angle of a regular heptagon isabout 51.4 degrees

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Octagon

1.Has eight sides2.Has twenty diagonals3.Has six triangles4.The sum of all interior angles equal 1080degrees5.The interior angle of a regular octagon is 135degrees6.The exterior angle of a regular octagon is 45degrees

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Nonagon

1.Has nine sides2.Has twenty-seven diagonals3.Has seven triangles4.The sum of all interior angles equal 1260 degrees5.The interior angle of a regular nonagon is 140degrees6.The exterior angle of a regular nonagon is 40degrees

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Decagon

1.Has ten sides2.Has thirty-five diagonals3.Has eight triangles4.The sum of all interior angles equal 1440degrees5.The interior angle of a regular decagon is 144degrees6.The exterior angle of a regular decagon is 36degrees

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Undecagon

1.Has eleven sides2.Has forty-four diagonals3.Has nine triangles4.The sum of all interior angles equal 1620degrees5.The interior angle of a regular undecagon is 147degrees6.The exterior angle of a regular undecagon is 33degrees

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Dodecagon

1.Has twelve sides2.Has fifty-four diagonals3.Has ten triangles4.The sum of all interior angles equal 1800degrees5.The interior angle of a regular dodecagon is 150degrees6.The exterior angle of a regular dodecagon is 30degrees

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Reflection:I really think I did a good job on thisproject. I worked hard on a lot ofthings, even drawing the picture on thetitle page, which was a hard thing tofigure out. It was a fun project, and Ienjoyed doing it. I worked at least acouple of days on it, putting in two orthree hours a day. Its a hard projectif you take into account all thedetails you have to focus on. I evenput in four more shapes so that I couldget a better grade because I reallywant to do well in this class. Atleast, I think I deserve a B+ or an AI dont want to seem over achieving butI want the best grade possible to makeyou, my parents and myself proud.