Lesson 1-6 Polygons

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

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°

Objectives Identify and name polygons Find perimeters of polygons

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

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

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

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

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

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

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

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

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)

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.

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