Properties and Attributes of Polygons

Transcription

1 Warm Up 1. A? is a three-sided polygon. triangle 2. A? is a four-sided polygon. quadrilateral Evaluate each expression for n = (n 4) (n 3) Solve for a a + 4a + 9a = 100 4

2 Learning Targets To find and use the measures of interior and exterior angles of polygons.

3 side of a polygon vertex of a polygon diagonal regular polygon concave convex Vocabulary

4 What is a polygon? A polygon is a closed plane figure formed by three or more segments.

5 Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal.

6 You can name a polygon by the number of its sides. The table shows the names of some common polygons.

7 Example 1A: Identifying Polygons Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides. polygon, hexagon polygon, heptagon not a polygon

8 Check It Out! Polygon or Not Polygon? Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides. not a polygon

9 Three Types of polygon: Equilateral polygons all sides are equal. Equiangular polygons all angles are equal. Regular polygons both equilateral & equiangular. N.B. If a polygon is not regular, it is called irregular.

10 There are 2 shapes of regular polygons: A polygon is concave If it caves in, it is concave. A polygon is convex If it does not cave in, it is convex.

11 Example 2A: Classifying Polygons Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. irregular, convex regular, convex irregular, concave

12 Check It Out! Example 2a Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. regular, convex

13 To find the sum of the interior angle measures of a convex polygon, draw all possible diagonals from one vertex of the polygon. This creates a set of triangles. The sum of the angle measures of all the triangles equals the sum of the angle measures of the polygon.

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15 The formula of the sum of the angle measures of all these triangles is (n 2)180.

16 Example 3B: Finding Interior Angle Measures and Sums in Polygons Find the measure of each interior angle of a regular 12-gon. n =12. Step 1 Find the sum of the interior angle measures. (12 2)180 = 1800 Step 2 Find the measure of one interior angle /12 =150

17 Finding Interior Angle Measures and Sums in Polygons

18 Finding Interior Angle Measures and Sums in Polygons Try this one: Find the sum of the interior angle measures of the following convex polygons and one interior angle gon, n=13

19 Finding Interior Angle Measures and Sums in Polygons

20 Finding Interior Angle Measures and Sums in Polygons Try this one: The sum of the measures of the interior angles of a convex polygon is 1200 deg. Classify the number of sides.

21 Finding Interior Angle Measures and Sums in Polygons Polygon Interior Angles Theorem The sum of the measures of interior angles of a quadrilateral is 360 degrees. Find the value of x.

22 Finding Interior Angle Measures and Sums in Polygons

23 Exterior Angles of Polygon: The sum of the exterior angle measures is 360.

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25 Example 4A: Finding Interior Angle Measures and Sums in Polygons Find the measure of each exterior angle of a regular 20-gon. The measure of each exterior angle of a regular 20-gon is 18.

26 Example 4A: Finding Interior Angle Measures and Sums in Polygons

27 Check It Out! Example 4b Find the value of r in polygon JKLM.

28 Try this one:

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30 Class work 7-1: Due next class 1/11/2017 (B) and 1/12/2017 (A) Question # 3, 4, 7, 9, 11, 13, 15, 17, 19, 21

31 Class work 7-1: Due next class 1/11/2017 (B) and 1/12/2017 (A) Question # 3, 4, 7, 9, 11, 13, 15, 17, 19, 21

32 Class work 7-1: Due next class 1/11/2017 (B) and 1/12/2017 (A) Question # 3, 4, 7, 9, 11, 13, 15, 17, 19, 21