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Lesson 1-6 Polygons

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5-Minute Check on Lesson 1-5 Transparency 1-6 Click the mouse button or press the Space Bar to display the answers. Refer to the figure for questions 1 through 3. 1.Name two acute vertical angles. 2.Name a linear pair whose vertex is E. 3.Name an angle supplementary to BEC. 4.If 1 and 2 are supplementary and the measure of 1 is twice that of 2, then find the measures of both angles. 5.If RS ST and SV is the angle bisector of RST, what is the m TSV? 6. If two angles are congruent and supplementary, then they must be Standardized Test Practice: A C B D two right angles two acute angles two obtuse angles an acute and an obtuse angle 48° A B C D E

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5-Minute Check on Lesson 1-5 Transparency 1-6 Click the mouse button or press the Space Bar to display the answers. Refer to the figure for questions 1 through 3. 1.Name two acute vertical angles. 2.Name a linear pair whose vertex is E. 3.Name an angle supplementary to BEC. 4.If 1 and 2 are supplementary and the measure of 1 is twice that of 2, then find the measures of both angles. 5.If RS ST and SV is the angle bisector of RST, what is the m TSV? 6. If two angles are congruent and supplementary, then they must be Standardized Test Practice: A C B D two right angles two acute angles two obtuse angles an acute and an obtuse angle 48° A B C D E m TSV = ½ m RST = ½(90) = 45° m AEB = m DEC = 48° Samples: AEB and AED or BEC and CED Either AEB or DEC m 1 + m 2 = 180 supplementary m 1 = 2m 2 so 2m 2 + m 2 = 180 3m 2 = 180 m 2 = 60° m 1 = 120°

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Objectives Identify and name polygons Find perimeters of polygons

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Vocabulary Polygon – a closed figure whose sides are all line segments n-gon – a polygon with n sides Concave – any line aligned to the sides passes through the interior Convex – not concave (“side line” passes through interior) Regular polygon – a convex polygon with all segments congruent & all angles congruent Irregular polygon – not regular Perimeter – the sum of the lengths of sides of the polygon

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Not a Polygon Figure is not closed Sides are not line segments

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ConcaveConvex IrregularRegular Side extended goes through interior Interior Angle > 180° Not Concave All extended sides stay outside interior All Interior Angles less than 180° All Sides same All Angles same Not Regular Polygons

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Perimeter Once around the figure If regular, then a = b = c = d = e = f and P = 6a P = a + b + c + d + e + f a b c d e f

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Names of Polygons Number of Sides Name Sum of Interior Angles 3Triangle180 4Quadrilateral360 5Pentagon540 6Hexagon720 7Heptagon900 8Octagon1080 9Nonagon1260 10Decagon1440 12Dodecagon1800 nN-gon(n-2) 180

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Example 6-1a Name the polygon by its number of sides. Then classify it as convex or concave, regular or irregular. There are 4 sides, so this is a quadrilateral. No line containing any of the sides will pass through the interior of the quadrilateral, so it is convex. The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular

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Example 6-1b Name the polygon by its number of sides. Then classify it as convex or concave, regular or irregular. There are 9 sides, so this is a nonagon. A line containing some of the sides will pass through the interior of the nonagon, so it is concave. The sides are not congruent, so it is irregular. Answer: nonagon, concave, irregular

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Example 6-2a CONSTRUCTION A masonry company is contracted to lay three layers of decorative brick along the foundation for a new house given the dimensions below. Find the perimeter of the foundation. Add the side’s lengths

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Example 6-4a The width of a rectangle is 5 less than twice its length. The perimeter is 80 centimeters. Find the length of each side. Let represent the length. Then the width is. P = l + w + l + w = 2(l + w)

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Example 6-4b Perimeter formula for rectangle Multiply. Simplify. Add 10 to each side. Divide each side by 6. Answer: The length is 15 cm. By substituting 15 for, the width becomes 2(15) – 5 or 25 cm.

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Summary & Homework Summary: –A polygon is a closed figure made of line segments –The perimeter of a polygon is the sum of the lengths of its sides Homework: –pg 49-50: 12-21, 29-31, 33

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