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Identifying and Classifying Polygons: Regular vs. Not Regular

Learn to identify and classify polygons, including regular and not regular polygons. Discover how to find the angle measures of regular polygons.

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Identifying and Classifying Polygons: Regular vs. Not Regular

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  1. Warm Up True or false? 1. Some trapezoids are parallelograms. 2. Some figures with 4 right angles are squares. 3. Some quadrilaterals have only one right angle. false true true

  2. Learn to identify regular and not regular polygons and to find the angle measures of regular polygons.

  3. Vocabulary polygon regular polygon diagonal

  4. A polygon is a closed plane figure formed by three or more line segments. A regular polygon is a polygon in which all sides are congruent and all angles are congruent. Polygons are named by the number of their sides and angles.

  5. Additional Example 1A: Identifying Polygons Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular. The shape is a closed plane figure formed by 3 or more line segments. polygon There are 5 sides and 5 angles. pentagon All 5 sides do not appear to be congruent. not regular

  6. Additional Example 1B: Identifying Polygons Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular. The shape is a closed plane figure formed by 3 or more line segments. polygon There are 8 sides and 8 angles. octagon The sides and angles appear to be congruent. regular

  7. Check It Out: Example 1A Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular. There are 4 sides and 4 angles. quadrilateral The sides and angles appear to be congruent. regular

  8. Check It Out: Example 1B Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular. There are 4 sides and 4 angles. quadrilateral All 4 sides do not appear to be congruent. not regular

  9. You can divide any quadrilateral into two triangles by drawing a diagonal, a line segment that connects two non-adjacent vertices. The sum of the interior angle measures in a triangle is 180°, so the sum of the interior angle measures in a quadrilateral is 360°.

  10. 1 Understand the Problem Additional Example 2: Problem Solving Application Malcolm designed a wall hanging that was a regular 9-sided polygon (called a nonagon). What is the measure of each angle of the nonagon? The answer will be the measure of each angle in a nonagon. List the important information: • A regular nonagon has 9 congruent sides and t 9 congruent angles.

  11. 2 Make a Plan 3 Solve Additional Example 2 Continued Make a table to look for a pattern using regular polygons. Draw some regular polygons and divide each into triangles.

  12. Reading Math The prefixes in the names of the polygons tell you how many sides and angles there are. tri- = three quad- = four penta- = five hexa- = six octa- = eight Additional Example 2 Continued 720°

  13. 3 Solve Cont. Additional Example 2 Continued The number of triangles is always 2 fewer than the number of sides. A nonagon can be divided into 9 – 2 = 7 triangles. The sum of the interior angle measures in a nonagon is 7  180° = 1,260°. So the measure of each angle is 1,260° ÷ 9 = 140°.

  14. 4 Additional Example 2 Continued Look Back Each angle in a nonagon is obtuse. 140° is a reasonable answer, because an obtuse angle is between 90° and 180°.

  15. 1 Understand the Problem Check It Out: Example 2 Sara designed a picture that was a regular 6-sided polygon (called a hexagon). What is the measure of each angle of the hexagon? The answer will be the measure of each angle in a hexagon. List the important information: • A regular hexagon has 6 congruent sides and 6 congruent angles.

  16. 2 Make a Plan 3 Solve Check It Out: Example 2 Continued Make a table to look for a pattern using regular polygons. Draw some regular polygons and divide each into triangles.

  17. 3 Solve Cont. Check It Out: Example 2 Continued The number of triangles is always 2 fewer than the number of sides. A hexagon can be divided into 6 – 2 = 4 triangles. The sum of the interior angles in a octagon is 4  180° = 720°. So the measure of each angle is 720° ÷ 6 = 120°.

  18. 4 Check It Out: Example 2 Continued Look Back Each angle in a hexagon is obtuse. 120° is a reasonable answer, because an obtuse angle is between 90° and 180°.

  19. Lesson Quiz 1. Name each polygon and tell whether it appears to be regular or not regular. 2. What is the measure of each angle in a regular dodecagon (12-sided figure)? nonagon, regular; octagon, not regular 150°

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