David Vundi Mathematics Teacher Classify Polygons GEOMETRY

David Vundi Objective Standard 3: Analyze properties of 2-D shapes Standard 8: Use the language of math to express ideas Find the perimeter and area of common plane figures and use a general problem-solving plan

David Vundi Polygons Polygons are two-dimensional geometric figures with these characteristics: They are made of straight line segments called sides. Each segment touches exactly two other segments, one at each of its endpoints. They are closed – they divide the plane into two distinct regions, one “inside” and the other “outside” the polygon.

David Vundi Polygons: How many side? Triangle 3 Quadrilateral 4 Pentagon5 Hexagon 6 Heptagon7 Octagon 8 Nonagon 9 Decagon 10 Dodecagon 12 n-gon n on 7

David Vundi Finding polygons Each corner of a polygon, where two sides meet, is called a vertex. The plural of vertex is vertices. In the following activities, you will search for polygons in several figures. You’ll calculate a score for each figure by adding the following: a. 3 points for each triangle b. 4 points for each quadrilateral c. 5 points for each pentagon d. 6 points for each hexagon

David Vundi Properties of Polygon Concave polygons look like they are collapsed or have one or more angles dented in. Any polygons that has an angle measuring more than 180  is concave.

David Vundi Properties of Polygon Regular polygons have sides that are all the same length and angles that are all the same size. The polygons below are not regular. Such polygons are referred to as irregular.

David Vundi Properties of Polygon A polygon has line symmetry, or reflection symmetry, if you can fold it in half along a line so the two halves match exactly. The “folding line” is called the line of symmetry.

David Vundi Polygon-Classification Game Venn diagrams use circles to represent relationships among sets of objects. They are named after John Venn ( ) of England. Venn, a priest and historian, published two books on logic in the 1880s. Venn diagrams can be used to solve certain types of logic puzzles.

Polygon-Classification Game Regular Symmetry Concave

David Vundi Dividing Polygons Into Triangles Polygons with any number of sides can be divided up into triangles. Here are a few examples:

David Vundi Example Each figure is a regular polygon. Find the value of x. x 2 + x x x 2 + 3x x 2 + x + 2

David Vundi Perimeter, Circumference and Area Perimeter and circumference is what you draw, and the units are linear. It is the distance around a figure. Area is what you color, and the units are square units. It is the amount of surface covered by a figure.

David Vundi Square: Length of each side is s Perimeter, P = 4s Area, A = s 2 Area and Perimeter of Square

David Vundi Rectangle: Length, l, and width, w Perimeter, P = 2l + 2w Area, A = lw Area and Perimeter of Rectangle

David Vundi Triangle: Side lengths a, b, and c, base is b, and height is h Perimeter, P = a + b + c Area, A = ½ bh ac b h Area and Perimeter of Trinagle

David Vundi Circle: Diameter is d and radius is r Circumference, C =  d or 2  r Area, A =  r 2 Area and Perimeter of Circle

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