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Transcript
Lesson 1-6 Polygons 5-Minute Check on Lesson 1-5 Transparency 1-6 A Refer to the figure for questions 1 through 3. 1. Name two acute vertical angles. D 48° E 2. Name a linear pair whose vertex is E. B C 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. Standardized Test Practice: If two angles are congruent and supplementary, then they must be A two right angles B two acute angles C two obtuse angles D an acute and an obtuse angle Click the mouse button or press the Space Bar to display the answers. 5-Minute Check on Lesson 1-5 Transparency 1-6 A Refer to the figure for questions 1 through 3. 1. Name two acute vertical angles. D 48° m AEB = m DEC = 48° E 2. Name a linear pair whose vertex is E. Samples: AEB and AED or BEC and CED B C 3. Name an angle supplementary to BEC. Either AEB or DEC 4. If 1 and 2 are supplementary and the measure of 1 is twice that of 2, then find the measures of both angles. m1 + m2 = 180 supplementary m1 = 2m2 so 2m2 + m2 = 180 3m2 = 180 m2 = 60° m1 = 120° 5. If RS ST and SV is the angle bisector of RST, what is the m TSV? m TSV = ½ m RST = ½(90) = 45° 6. Standardized Test Practice: If two angles are congruent and supplementary, then they must be A two right angles B two acute angles C two obtuse angles D an acute and an obtuse angle Click the mouse button or press the Space Bar to display the answers. 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 Polygons Side extended goes through interior Concave Convex Not Concave All extended sides stay outside interior Interior Angle > 180° All Interior Angles less than 180° Irregular Not Regular Regular All Sides same All Angles same Perimeter P=a+b+c+d+e+f e f d Once around the figure a c b If regular, then a = b = c = d = e = f and P = 6a Names of Polygons Number of Sides Name Sum of Interior Angles 3 4 Triangle Quadrilateral 180 360 5 6 7 Pentagon Hexagon Heptagon 540 720 900 8 9 Octagon Nonagon 1080 1260 10 12 n Decagon Dodecagon N-gon 1440 1800 (n-2) • 180 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 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 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 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) . Perimeter formula for rectangle Multiply. Simplify. Add 10 to each side. Divide each side by 6. The length is 15 cm. By substituting 15 for , the width becomes 2(15) – 5 or 25 cm. Answer: 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