8-7 Polygons Course 1 Warm Up Problem of the Day Lesson Presentation

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

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

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

Vocabulary polygon regular polygon

Triangles and quadrilaterals are examples of 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.

An equilateral triangle has three congruent sides. Remember!

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

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

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

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

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 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.

Additional Example 2 Continued 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 720° 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 Reading Math

Additional Example 2 Continued Solve Cont. 3 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 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 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.

Check It Out: Example 2 Continued 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.

Check It Out: Example 2 Continued Solve Cont. 3 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°.

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°.

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°