Download Polygons and Coordinate Plane

Polygons and Coordinate Plane
Rylie Duggan
Lake Shore High School
Rani Brikho
Sterling Heights High School
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Real World Application
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Common Core State Standard
Math.Content.6.G.A.3
Grade
Geometry
Subsection
Topic
Case #13 (Polygons and Coordinate Plane)
Draw polygons in the coordinate plane given coordinates for the
vertices; use coordinates to find the length of a side joining points
with the same first coordinate or the same second coordinate. Apply
these techniques in the context of solving real-world and
mathematical problems.
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What is a Polygon?
• A polygon is a closed plane shape (two-dimensional) with straight
sides.
http://mathforum.org/sum95/math_and/poly/reg_polygons.html
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http://www.clker.com/cliparts/8/d/9/4/11949895841082690832yield.svg.hi.png
Types of Polygons
•
•
•
•
Triangle – 3 sides
Quadrilateral – 4 sides
Pentagon – 5 sides
Hexagon – 6 sides
https://sp.yimg.com/ib/th?id=HN.608011088620293541&pid=15.1&P=0
https://sp.yimg.com/ib/th?id=HN.6080103284049847
http://media-cache-ec0.pinimg.com/736x/84/e1/65/84e1654f95c8637c62c281b523296378.jpg
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Types of Polygons Cont.
• Heptagon – 7 sides
• Octagon – 8 sides
• Nonagon – 9 sides
https://sp.yimg.com/ib/th?id=HN.607987217191536609&pid=15.1&P=0
• Decagon – 10 sides
• Undecagon – 11 sides
• Dodecagon – 12 sides
https://sp.yimg.com/ib/th?id=HN.607988879343684625&pid=15.1&P=0
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N-gon
• A polygon with n sides, or a polygon with an unknown number of
sides
• Often used for polygons with many sides, such as a 23-gon or a
46-gon
14-gon
14-gon
http://etc.usf.edu/clipart/37300/37390/14-gon_37390.htm
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Convex vs. Concave
• Convex polygons are polygons with no diagonal outside the
polygon
• Concave polygons are polygons with at least one diagonal outside
the polygon
http://mathworld.wolfram.com/ConvexPolygon.html
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Exterior Angles
• Exterior angle - the angle formed by any side of a polygon and the extension
of its adjacent side
• Exterior angles always add up to 360°
One Exterior Angle:
360/n
http://www.ducksters.com/kidsmath/angles_glossary.php
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Interior Angles
• Interior angle – an angle of a polygon contained between two
adjacent sides
Sum of Interior Angles:
(n-2)180
One Interior Angle:
180-360/n
(6-2)180
(4)180
180-360/6
180-60
120
720
http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/polygonsrev5.shtml
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Coordinate Plane
• The plane containing the horizontal x-axis and the vertical y-axis
• Divided into 4 quadrants
II
II
III
IV
http://en.wikibooks.org/wiki/Intermediate_Algebra/The_Coordinate_(Cartesian)_Plane
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Creating a Polygon
• Plot points: (2,3) (-2,3) (-2,-3) (2,-3)
• Connect points to form a rectangle
http://domathtogether.com/wp-content/uploads/2012/10/coordinate-plane1.png
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Using Coordinates to Find Distance Between Two
Points
• Find the difference between two points
2 - (-2)=4
Distance = 4 units
(-2,3)
(2,3)
B
C
http://domathtogether.com/wp-content/uploads/2012/10/coordinate-plane1.png
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Recap
•
•
•
•
•
Polygons: 2-D shapes with straight sides
N-Gon
Exterior angles: 360/n and always add up to 360º
Interior angles: 180-360/n and (n-2)180
Distance: difference between two coordinates
Works Cited
"Common Core." IXL. N.p., n.d. Web. 17 Feb. 2015. <http://www.ixl.com/standards/commoncore/math/grade-6>
"Polygons - Polygon Basics - In Depth." Polygons - Polygon Basics - In Depth. N.p., n.d. Web. 18
Feb. 2015. <http://www.math.com/school/subject3/lessons/S3U2L1DP.html>
"The Coordinate Plane - Math Open Reference." The Coordinate Plane - Math Open Reference.
N.p., n.d. Web. 18 Feb. 2015. <http://www.mathopenref.com/coordplane.html>
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Questions?
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Quiz Time!
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Is this a convex polygon or a concave polygon?
http://etc.usf.edu/clipart/42600/42623/irregoct_42623_lg.gif
Concave
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What is the measure of one interior angle of this
pentagon? (HINT: Use the formula 180-360/n)
180-360/5
180-72
108
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http://www.ixl.com/math/grade-6/coordinate-graphs-review
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What is the distance between these two points?
(4,4)
5 units
(2,1)
(7,1)
http://www.ixl.com/math/grade-6/distance-between-two-points
(4,-3)
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