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Transcript
8-7 8-7 Polygons Polygons Warm Up Problem of the Day Lesson Presentation Course Course 11 8-7 Polygons Warm Up True or false? 1. Some trapezoids are parallelograms. false 2. Some figures with 4 right angles are squares. true 3. Some quadrilaterals have only one right angle. true Course 1 8-7 Polygons Problem of the Day Four square tables pushed together can seat either 8 or 10 people. How many people could 12 square tables pushed together seat? 14, 16, or 26 people Course 1 8-7 Polygons Learn to identify regular and not regular polygons and to find the angle measures of regular polygons. Course 1 8-7 Polygons Vocabulary polygon regular polygon Course 1 8-7 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 8-7 Polygons Remember! An equilateral triangle has three congruent sides. Course 1 8-7 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. 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 Course 1 8-7 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. 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 Course 1 8-7 Polygons 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 Course 1 8-7 Polygons 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 Course 1 8-7 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°. Course 1 8-7 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 t 9 congruent angles. Course 1 8-7 Polygons Additional Example 2 Continued 2 Make a Plan Make a table to look for a pattern using regular polygons. 3 Solve Draw some regular polygons and divide each into triangles. Course 1 8-7 Polygons Additional Example 2 Continued 720° Reading Math The prefixes in the names of the polygons tell you how many sides and angles there are. Course 1 tri- = three quad- = four penta- = five hexa- = six octa- = eight 8-7 Polygons Additional Example 2 Continued 3 Solve Cont. 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°. Course 1 8-7 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°. Course 1 8-7 Polygons 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? 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. Course 1 8-7 Polygons Check It Out: Example 2 Continued 2 Make a Plan Make a table to look for a pattern using regular polygons. 3 Solve Draw some regular polygons and divide each into triangles. Course 1 8-7 Polygons Check It Out: Example 2 Continued 3 Solve Cont. 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°. Course 1 8-7 Polygons Check It Out: 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°. Course 1 8-7 Polygons Lesson Quiz 1. Name each polygon and tell whether it appears to be regular or not regular. nonagon, regular; octagon, not regular 2. What is the measure of each angle in a regular dodecagon (12-sided figure)? 150° Course 1