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Properties and Attributes of Polygons

Properties and Attributes of Polygons. Warm Up 1. A ? is a three-sided polygon. 2. A ? is a four-sided polygon. Evaluate each expression for n = 6. 3. ( n – 4) 12 4. ( n – 3) 90 Solve for a . 5. 12 a + 4 a + 9 a = 100. triangle. quadrilateral. 24. 270. 4.

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Properties and Attributes of Polygons

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  1. Properties and Attributes of Polygons

  2. Warm Up 1.A ? is a three-sided polygon. 2. A ? is a four-sided polygon. Evaluate each expression for n = 6. 3. (n – 4) 12 4. (n – 3) 90 Solve for a. 5. 12a + 4a + 9a = 100 triangle quadrilateral 24 270 4

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

  4. 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.

  5. All the sides are congruent in an equilateral polygon. All the angles are congruent in an equiangular polygon. A regular polygonis one that is both equilateral and equiangular. If a polygon is not regular, it is called irregular. Irregular polygon – not all sides have same length and not all angles have same measure

  6. A polygon is concave if it has an angle caving in. A polygon is convex if it has no angles caving in. A regular polygon is always convex.

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

  8. Polygon Angle Sum Theorem

  9. Example 3A: Finding Interior Angle Measures and Sums in Polygons Find the sum of the interior angle measures of a regular heptagon. (n – 2)180° Polygon  Sum Thm. (7 – 2)180° A heptagon has 7 sides, so substitute 7 for n. 900° Simplify.

  10. Example 3B: Finding Interior Angle Measures and Sums in Polygons Find the measure of each interior angle of a regular 16-gon. Step 1 Find the sum of the interior angle measures. (n – 2)180° Polygon  Sum Thm. Substitute 16 for n and simplify. (16 – 2)180° = 2520° Step 2 Find the measure of one interior angle. The int. s are , so divide by 16.

  11. Remember! An exterior angle is formed by one side of a polygon and the extension of a consecutive side.

  12. In the polygons below, an exterior angle has been measured at each vertex. Notice that in each case, the sum of the exterior angle measures is 360°.

  13. measure of one ext.  = Example 4A: Finding Interior Angle Measures and Sums in Polygons Find the measure of each exterior angle of a regular 20-gon. A 20-gon has 20 sides and 20 vertices. sum of ext. s = 360°. Polygon  Sum Thm. A regular 20-gon has 20  ext. s, so divide the sum by 20. The measure of each exterior angle of a regular 20-gon is 18°.

  14. Tessellations • A tessellation (also called tiling) is created when a polygon is repeated over and over again covering an area with no gaps or overlaps

  15. Tiling Polygons You can only tile polygons if they follow these rules: • All polygons must be regular • The interior angles of the polygons meeting at a vertex must equal 360.

  16. Homework • Pg 31, #’s 33-36 • Page 52-59, #’s 1-15, 17, 18, 21-23, 25

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