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Identifying Polygons and Regularity

Learn to identify and classify polygons, determine if they are convex or concave, and identify regular polygons. Practice solving problems involving interior angles and regularity of polygons.

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Identifying Polygons and Regularity

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  1. State whether the figure is a polygon. If it is not, explain why. Not D – has a side that isn’t a segment – it’s an arc. Not E– because two of the sides intersect only one other side. Not F because some of its sides intersect more than two sides/ Warm UP: Identifying Polygons Figures A, B, and C are polygons.

  2. Polygons are named by the number of sides they have – MEMORIZE

  3. Polygons are named by the number of sides they have – MEMORIZE

  4. Identify the polygon and state whether it is convex or concave. Convex or concave? CONCAVE CONVEX

  5. Decide whether the following polygons are regular. Identifying Regular Polygons Heptagon is equilateral, but not equiangular, so it is NOT a regular polygon. Pentagon is equilateral and equiangular, so it is a regular polygon. Equilateral, but not equiangular, so it is NOT a regular polygon.

  6. 6.1 Polygons Objectives: • Identify, name, and describe polygons • Use the sum of the measures of the interior angles of a quadrilateral.

  7. The sum of the measures of the interior angles of a quadrilateral is 360°. Theorem 6.1: Interior Angles of a Quadrilateral m1 + m2 + m3 + m4 = 360°

  8. x°+ 2x° + 70° + 80° = 360° 3x + 150 = 360 3x = 210 x = 70 Sum of the measures of int. s of a quadrilateral is 360° Combine like terms Subtract 150 from each side. Divide each side by 3. Ex. 1: Use the information in the diagram to solve for x. 80° 70° 2x° x°

  9. Ex. 2: Use the information in the diagram to solve for x. 5x + 7x + 50 + 70 = 360 12x + 120 = 360 12x = 240 X = 20 50 7x 5x 70

  10. Ex. 3: Use the information in the diagram to solve for x. 90 + 87 + 93 + x = 360 270 + x = 360 x = 90 x 87 93

  11. 3x + 2x + 3x + 2x = 360 10x = 360 x = 36 Ex. 4: Use the information in the diagram to solve for x. 2x 3x 3x 2x

  12. 2x + 4x +2x + 4x = 360 12x = 360 x = 30 Substitute 2(30) = 60 4 (30) = 120 Ex. 5: Find the measure of each angle in the parallelogram. 2x 4x 2x 4x

  13. Assignment • Solve the remaining problems independently • Reminder:2nd Nine weeks benchmark on Thursday

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