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Classifying and Identifying Polygons: Types, Sides, and Characteristics

This section covers the classification and identification of polygons based on their types, number of sides, and characteristics such as convexity and regularity. Examples and explanations are provided to help understand the concepts.

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Classifying and Identifying Polygons: Types, Sides, and Characteristics

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  1. Section 1.6 Classify Polygons Each side intersects exactly two other sides, but only at their end points Definition of a polygon:A polygon is a closed figure formed by a finite number of segments such that: The sides that have a common endpoint are noncollinear

  2. Section 1.6 Examples of Polygons

  3. Section 1.6 Types of Polygons Convex polygon – A polygon such that no line containing a side of the polygon contains a point in the interior of the polygon Concave polygon – A polygon that is simply not convex

  4. b. c. d. a. a. Some segments intersect more than two segments, so it is not a polygon. b. The figure is a convex polygon. c. Part of the figure is not a segment, so it is not a polygon. d. The figure is a concave polygon. EXAMPLE 1 Identify polygons Tell whether the figure is a polygon and whether it is convex or concave. SOLUTION

  5. EXAMPLE 1 Identify polygons Convex or Concave? Why?

  6. Section 1.6 Classify Polygons Polygons By Number of Sides

  7. Section 1.6 Classify Polygons In an equilateral polygon, all sides are congruent. IN an equiangular polygon, all angles in the interior of the polygon are congruent A regular polygon is a convex polygon that is both equilateral and equiangular

  8. a. b. a. The polygon has 6 sides. It is equilateral and equiangular, so it is a regular hexagon. b. The polygon has 4 sides, so it is a quadrilateral. It is not equilateral or equiangular, so it is not regular. EXAMPLE 2 Classify polygons Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning. SOLUTION

  9. The polygon has 12 sides, so it is a dodecagon. The sides are congruent, so it is equilateral. The polygon is not convex, so it is not regular. c. c. EXAMPLE 2 Classify polygons Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning. SOLUTION

  10. Sketch an example of a convex heptagon and an example of a concave heptagon. 1. for Examples 1 and 2 GUIDED PRACTICE ANSWER

  11. Classify the polygon shown at the right by the number of sides. Explain how you know that the sides of the polygon are congruent and that the angles of the polygon are congruent. 2. ANSWER Quadrilateral. They all have the same measure; they are all right angles. for Examples 1 and 2 GUIDED PRACTICE

  12. A table is shaped like a regular hexagon.The expressions shown represent side lengths of the hexagonal table. Find the length of a side. ALGEBRA 3x + 6 4x – 2 = 6 x – 2 = 8 x = EXAMPLE 3 Find side lengths SOLUTION First, write and solve an equation to find the value of x. Use the fact that the sides of a regular hexagon are congruent. Write equation. Subtract 3x from each side. Add 2 to each side.

  13. 3x + 6 3(8) + 6 = = 30 The length of a side of the table is 30inches. ANSWER EXAMPLE 3 Find side lengths Then find a side length. Evaluate one of the expressions when x = 8.

  14. 3. The expressions 8y° and ( 9y – 15 )° represent the measures of two of the angles in the table in Example 3. Find the measure of an angle. ANSWER 120o for Example 3 GUIDED PRACTICE

  15. EXAMPLE 3 Find side lengths Example: A rack of pool balls is shaped like an equilateral triangle. Find the length of a side.

  16. What is a polygon? What is the difference between convex and concave polygons? When is a polygon regular? Section 1.6 Summary

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