7-7 Polygons Course 1 Warm Up Problem of the Day Lesson Presentation

Course 1 7-7 Polygons Learn to identify regular and not regular polygons and to find the angle measures of regular polygons.

Insert Lesson Title Here Course 1 7-7 Polygons Insert Lesson Title Here Vocabulary polygon regular polygon

Course 1 7-7 Polygons Triangles and quadrilaterals are examples of polygons. 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.

Course 1 7-7 Polygons

Additional Example 1A: Identifying Polygons Course 1 7-7 Polygons 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. A. The shape is a closed plane figure formed by three or more line segments. polygon There are five sides and five angles. pentagon All 5 sides do not appear to be congruent. Not regular

Additional Example 1B: Identifying Polygons Course 1 7-7 Polygons 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. B. The shape is a closed plane figure formed by three or more line segments. polygon There are eight sides and eight angles. octagon The sides and angles appear to be congruent. regular

7-7 Polygons Try This: Example 1A Course 1 7-7 Polygons Try This: 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. A. There are four sides and four angles. quadrilateral The sides and angles appear to be congruent. regular

7-7 Polygons Try This: Example 1B Course 1 7-7 Polygons Try This: 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. B. There are four sides and four angles. quadrilateral The sides and angles appear to be congruent. regular

Course 1 7-7 Polygons 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°.

Understand the Problem Course 1 7-7 Polygons 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? 1 Understand the Problem The answer will be the measure of each angle in a nonagon. List the important information: A regular nonagon has 9 congruent sides and 9 congruent angles.

Additional Example 2 Continued Course 1 7-7 Polygons Additional Example 2 Continued 2 Make a Plan Make a table to look for a pattern using regular polygons. Solve 3 Draw some regular polygons and divide each into triangles.

Additional Example 2 Continued Course 1 7-7 Polygons Additional Example 2 Continued 720°

Additional Example 2 Continued Course 1 7-7 Polygons 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°.

Additional Example 2 Continued Course 1 7-7 Polygons Additional Example 2 Continued 4 Look Back Each angle in a nonagon is obtuse. 140° is a reasonable answer, because an obtuse angle is between 90° and 180°.

Understand the Problem Course 1 7-7 Polygons Try This: Additional 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? 1 Understand the Problem 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.

Try This: Example 2 Continued Course 1 7-7 Polygons Try This: Example 2 Continued 2 Make a Plan Make a table to look for a pattern using regular polygons. Solve 3 Draw some regular polygons and divide each into triangles.

Try This: Example 2 Continued Course 1 7-7 Polygons Try This: Example 2 Continued

Try This: Example 2 Continued Course 1 7-7 Polygons Try This: 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°.

Try This: Example 2 Continued Course 1 7-7 Polygons Try This: Example 2 Continued 4 Look Back Each angle in a hexagon is obtuse. 120° is a reasonable answer, because an obtuse angle is between 90° and 180°.

Insert Lesson Title Here Course 1 7-7 Polygons Insert Lesson Title Here 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°