(page 446-449) Indicator  G2: Properties of 2- dimensional figures.

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Presentation transcript:

(page ) Indicator  G2: Properties of 2- dimensional figures

The size and shape of each state in the United States is different. Analyze the shapes of the states in both groups below. Group 1Group 2 1- Utah2-Florida 1-Wyoming2-Texas 1- New Mexico 2-Indiana 1-Colorado2- North Carolina What are the differences between the shapes in the two groups?

On the previous slide, the states from group 1 are polygons. A polygon is a simple, closed figure formed by 3 or more straight lines. A simple figure does not have lines that cross each other. PolygonsNot Polygons Line segments are sides Sides meet at endpoints Points of intersection are vertices Sides overlap Figure is open Sides are curved

Polygons are classified by the number of sides they have. Words pentagonhexagonheptagonoctagonnonagondecagon Number of sides Models

A polygon that has all sides congruent and all angles congruent is called a regular polygon. Equilateral triangles and squares are examples of regular polygons.

Reminder: The sum of all angles in a triangle is 180º and in a quadrilateral is 360º. To find the measure of the angles in a regular polygon: 1.Draw all the diagonals from ONE vertex & count the number of triangles. (Each Triangle= 180 º) 2.Find the sum of the angle measures in the polygon. 3.Find the measure of each angle by dividing by the number of angles Triangles 3 × 180º = 540º 5n = n= 108 The measure of each angle in a regular pentagon is 108 º.

SidesTrianglesAngle sum Each angle ° of regular polygon 311 x 180 = 180°180/3 = 60° 422 x 180 = 360°360/4 = 90° 533 x 180 = 540°540/5 = 108° 6 N

One more thing… A tessellation is a pattern of polygons that fit together with no overlaps and no holes. The sum of the measures of the angles where the vertices meet in a tessellation is 360 º 135 º 90 º º

Homework Page #8-28 even, all & Extra Credit Tessellation –(Must be in color)