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Transcript: INTRODUCTION TO POLYGON INTRODUCTION TO POLYGON IS IT A POLYGON? IS IT A POLYGON? Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). Polygon (straight sides) Not a Polygon (has a curve) Not a Polygon (open, not closed) POLYGON POLYGON DEFINITION DEFINITION Polygon comes from Greek. Poly- means "many" and -gon means "angle" Pictures Pictures TYPES OF POLYGON TYPES OF POLYGON A. CONCAVE AND CONVEX B. SIMPLE AND COMPLEX C. REGULAR AND IRREGULAR A. CONCAVE & CONVEX A. CONCAVE & CONVEX A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°. If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a "cave" in it) CONVEX CONVEX CONCAVE CONCAVE B. SIMPLE & COMPLEX B. SIMPLE & COMPLEX A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself! Many rules about polygons don't work when it is complex. SIMPLE SIMPLE COMPLEX COMPLEX C.REGULAR & IRREGULAR C.REGULAR & IRREGULAR A regular polygon has all angles equal and all sides equal, otherwise it is irregular REGULAR REGULAR IRREGULAR IRREGULAR MORE EXAMPLE MORE EXAMPLE Irregular Hexagon Concave Octagon Complex Polygon (a "star polygon", in this case a pentagram) Names of Polygons Names of Polygons A triangle has three sides and three angles Triangles Triangles A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides. Quadrilaterals Quadrilaterals A pentagon is a 5-sided Polygon (a flat shape with straight sides): Pentagon Pentagon hexagon is a 6-sided polygon (a flat shape with straight sides). Hexagon Hexagon An octagon is an 8-sided polygon (a flat shape with straight sides). First, have a play with an octagon: Octagon Octagon Nonagon (or Enneagon) Nonagon (or Enneagon) Decagon Decagon BSEDUCATION MATHEMATICS LACSON, JR. ABELARD C. THANK YOU!! THANK YOU!!

Polygon Presentation

Transcript: Acute Angles Polygon Presentation Convex AND Concave This is a nonagon with 5 acute angles, because an acute angle is less than , and it has five of them. This is an asymmetric nonagon because you aren't able to just pick a vertice/spot, draw a line straight across, and have the two sides be the same. Here are three examples of nonagons in real life! Regular AND Irregular Ending My Polygon... This is a nonagon with 9 reflexive angles, since a reflexive angle is any angle that is larger than 180 , but is less than 360 . My polygon is the nonagon. The nonagon has 9 sides. Therefore, it also has 9 angles. 140 / Obtuse By Ella Lichtenberg This is a nonagon with a right angle, since a right angle is , and it has one. The Nonagon Seminole Badge Interior Angle Sum of The Nonagon This is a regular nonagon because it doesn't have any of the qualites that an irregular nonagon has and yet it has the qualities of a normal nonagon. Symmetric AND Asymmetric This is a convex nonagon because there are no indents in it and it doesn't look like it has been cut out of. This is a nonagon with 9 obtuse angles, since an obtuse angle is any angle that is larger than 90 but less than 180 , and this nonagon has 9 of those. Thanks for Watching! Nonagons with Obtuse AND Reflexive Angles This is a concave nonagon since it has a large indent in it and it looks as if it was cut out of but it still has nine sides. The Nonagon Nonagons with Right AND Acute Angles Hong Kong $5.00 Coin This is an irregular nonagon because it is concave and has some other qualities that only irregular nonagons do, and it doesn't have any of the qualities of a regular nonagon even though it has nine sides since that doesn't really count. Equation: (Sides-2)180 = Interior Angle Sum OR Equation: (Sides-2)*180 = Interior Angle Sum OR Equation: (9-2)180 = 1,260 OR Equation: (9-2)*180 =1,260 Symmetry 220 / Reflexive This is a symmetric nonagon because at any vertice or spot on the nonagon you can draw a line straight across and both sides with be the same. Bottom of a Cup To find the interior angle sum of a nonagon, you simply need to subtract 2 from the number of sides, and then multiply that number, 7, by 180 to get the interior angle sum. So, the interior angle sum of a nonagon is 1,260 . Nonagons in Real Life Have a Great Rest of Your Day!

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