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Warm-Up

Warm-Up. 1). 2 ). 3 ). 4 ). Warm-Up. 1). 2 ). Warm-Up. 3 ). 4 ). Chapter 1 Sections 2 and 3. Points, Lines, and Planes Perimeter and Area. Vocabulary.

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Warm-Up

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  1. Warm-Up 1) 2) 3) 4)

  2. Warm-Up 1) 2)

  3. Warm-Up 3) 4)

  4. Chapter 1Sections 2 and 3 Points, Lines, and Planes Perimeter and Area

  5. Vocabulary Planes- A basic undefined term of geometry. Flat surfaces that extend indefinitely in all directions and have no thickness. Lines- A basic undefined term of geometry. Lines extend indefinitely and have no thickness or width. Points- A basic undefined term of geometry. Points have no size.

  6. Vocabulary Cont. Space- A boundless three-dimensional figure consisting of all of its surface points and all of its interior points. Coplanar-points on the same plane Area-The number of square units contained in the interior of a figure. Area = Length * Width Perimeter-The distance around a two-dimensional figure. Perimeter of a rectangle = 2(Length) + 2(Width) l w w l

  7. Example 1: Using the figure to answer the following questions. • Name a point that is not collinear to F and C. • Points A, B, or D • b) Identify a point that is not in the plane N. • Points E or F • c) What is the intersection of plane ADE and plane N ? • Line DA E F C D A B N

  8. y x Example 2: Draw and label a figure showing lines NP and QR intersecting at point S for points N(3, -1), P(5, 2), Q(-3, 1), and R(0, -4). P Q N R S

  9. Example 3: State whether each is best modeled by a point, line, or plane. • A star in the sky. • A point. • B) An ice skating rink. • A plane. • C) A telephone wire strung between two poles. • A line.

  10. Example 4: Mr. and Mrs. Pinel are planning a rectangular vegetable garden. They want the garden to have an area of at least 15 square yards, but they have only 18 yards of wire fence to surround it. What are the possible dimensions of the garden if all the fence is used and the sides have whole-number lengths? • a) Draw all possibilities. 1 2 3 4 5 4 5 4 6 6 5 8 8 7 7 5 4 8 3 7 6 2 1 1 1 2 2 8 3 3 6 7

  11. Example 4: Mr. and Mrs. Pinel are planning a rectangular vegetable garden. They want the garden to have an area of at least 15 square yards, but they have only 18 yards of wire fence to surround it. What are the possible dimensions of the garden if all the fence is used and the sides have whole-number lengths? b)Fill in the table. 1 8 8 * 1 = 8 2 7 7 * 2 = 14 3 6 6 * 3 = 18 5 5 * 4 = 20 4 5 4 4 * 5 = 20 6 3 3 * 6 = 18 7 2 2 * 7 = 14 8 1 1 * 8 = 8

  12. Example 4: Mr. and Mrs. Pinel are planning a rectangular vegetable garden. They want the garden to have an area of at least 15 square yards, but they have only 18 yards of wire fence to surround it. c) What are the possible dimensions of the garden if all the fence is used and the sides have whole-number lengths? 6 by 3 or 5 by 4.

  13. Example 5: Find the are and perimeter. 10 cm 4 cm Area = Length * Width A = 10 * 4 A = 40 cm^2 Perimeter = 2(Length) + 2(Width) P = 2(10) + 2(4) P = 20 + 8 P = 28 cm

  14. Example 6: Find the missing measure in each formula. P = 2l + 2w; l = 3, P = 16, w = ? P = 2l + 2w 16 = 2(3) + 2w 16 = 6 + 2w 10 = 2w 5 = w b) I = prt; p = 350, r = 6%, I = 42, t = ? I = prt 42 = 350(0.06)(t) 42 = 21(t) 2 = t

  15. Example 7: Find the maximum area for the given perimeter of a rectangle. State the length and width of the rectangle. Perimeter = 24 millimeters 1 mm 11 mm 1 * 11 = 11 mm^2 2 mm 10 mm 2 * 10 = 20 mm^2 3 mm 9 mm 3 * 9 = 27 mm^2 4 mm 8 mm 4 * 8 = 32 mm^2 5 mm 7 mm 5 * 7 = 35 mm^2 6 mm 6 mm 6 * 6 = 36 mm^2 The maximum area for the given perimeter is 36 mm^2 and the length and width are 6 mm by 6 mm. Short cut- If the perimeter is divisible by 4, then divide by 4 and square that number. EX: 24/4 = 6, Area is 6 * 6 = 36

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