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Chapter 1.6

Chapter 1.6. Classify Polygons. Key Terms: Polygon Sides Vertex Convex polygon Concave polygon Equilateral Equiangular Regular Polygon classifications. a. b. c. d. a. Some segments intersect more than two segments, so it is not a polygon. The figure is a convex polygon. b.

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Chapter 1.6

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  1. Chapter 1.6 Classify Polygons • Key Terms: • Polygon • Sides • Vertex • Convex polygon • Concave polygon • Equilateral • Equiangular • Regular • Polygon classifications

  2. a. b. c. d. a. Some segments intersect more than two segments, so it is not a polygon. The figure is a convex polygon. b. Part of the figure is not a segment, so it is not a polygon. c. 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

  3. 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

  4. 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.

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

  6. 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 Number of sides are 4, so it is a quadrilateral. All the angles have the same measure and they are all right angles, also all the sides have the same measure . The sides of the polygons are congruent and that angles of the polygon are congruent. for Examples 1 and 2 GUIDED PRACTICE

  7. 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.

  8. 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.

  9. 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. for Example 3 GUIDED PRACTICE SOLUTION First , write and solve an equation to find the value of y. Use the fact that that the angles of a regular hexagon are congruent. 8y = 9y – 15 Write equation 0 = y – 15 Subtract each side by 8y 15 = y Add 15 to each side

  10. ANSWER The measure of an angle is 120° for Example 3 GUIDED PRACTICE Then find an angle. Evaluate one the expression when y = 15° 8y = 8 · 15° = 120°

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