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Lesson 1-6

Lesson 1-6. Polygons. Transparency 1-6. 5-Minute Check on Lesson 1-5. A. Refer to the figure for questions 1 through 3. Name two acute vertical angles. Name a linear pair whose vertex is E. Name an angle supplementary to BEC .

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Lesson 1-6

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  1. Lesson 1-6 Polygons

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

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

  4. Objectives • Identify and name polygons • Find perimeters of polygons

  5. 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

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

  7. Polygons Side extended goes through interior Concave Convex Not Concave All extended sidesstay outside interior All Interior Angles less than 180° Interior Angle > 180° Irregular Regular All Sides same All Angles same Not Regular

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

  9. Names of Polygons

  10. 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

  11. 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

  12. Example 6-2a CONSTRUCTIONA 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

  13. Let represent the length. Then the width is . 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. P = l + w + l + w = 2(l + w)

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

  15. 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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