Transcript polygon
th 6 Grade Math Homework Chapter 7-7 Page 354 #1-8 & #23-29 (Spiral Review) Ch 7 Learning Goal: PLANE GEOMETRY • • • • • • • • • • • • Learn to describe the figures by using the terms of geometry (7-1) Learn to name, measure, classify, estimate and draw angles (7-2) Learn to understand relationship of angles (7-3) Learn to classify the different types of lines (7-4) Learn to classify triangles and solve problems involving angle and side measures of triangles (7-5) Learn to identify, classify, and compare quadrilaterals (7-6) Learn to identify regular and not regular polygons and to find the angle measures of regular polygons (7-7) Learn to recognize, describe, and extend geometric patterns (7-8) Learn to identify congruent figures and to use congruence to solve problems (7-9) Learn to use translations, reflections, and rotations to transform geometric shapes (7-10) Learn to identify line symmetry (7-11) Learn to identify tessellations and shapes that can tessellate (7-12) 7-7 Polygons Warm Up Problem of the Day Lesson Presentation Course 1 7-7 Polygons Warm Up True or false? 1. Some trapezoids are parallelograms. false 2. Some figures with 4 right angles are squares. true Course 1 7-7 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, 18, or 26 people Course 1 7-7 Polygons Today’s Learning Goal Assignment Learn to identify regular and not regular polygons and to find the angle measures of regular polygons. 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 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 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 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 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°. 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. Course 1 7-7 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 7-7 Polygons Additional Example 2 Continued 720° 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°. 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°. 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. 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. 3 Solve Draw some regular polygons and divide each into triangles. Course 1 7-7 Polygons 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°. 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°. 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. nonagon, regular; octagon, not regular 2. What is the measure of each angle in a regular dodecagon (12-sided figure)? 150° Course 1