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Chapter 4

Chapter 4. Parallels. Objective: Describe relationships among lines, parts of lines and planes. 4-1. Parallel Lines and Planes. plane EFG. 4-2. Parallel Lines and Transversals.

adrienne-roderick
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Chapter 4

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  1. Chapter 4 Parallels

  2. Objective: Describe relationships among lines, parts of lines and planes. 4-1 Parallel Lines and Planes

  3. plane EFG

  4. 4-2 Parallel Lines and Transversals Objective: Identify the relationships among pairs of interior and exterior angles formed by two parallel lines and a transversal.

  5. Alternate exterior angles Consecutive interior angles

  6. -4x -4x -x – 5 = -29 +5 +5 -x = -24 x = 24

  7. Objective: Identify the relationships among pairs of corresponding angles. Angles 7 and 8 are called corresponding angles.

  8. +6 +6 96 = 3x 3 3 32 = x

  9. Objective: Identify conditions that produce parallel lines.

  10. 13x – 8 = 12x + 4 -12x -12x x – 8 = 4 +8 +8 x = 12

  11. 2x + 10 + 5x + 2 = 180 7x + 12 = 180 -12 -12 7x = 168 x = 24

  12. Objectives: Find the slopes of lines. Use slope to identify parallel and perpendicular lines.

  13. Slope – the ratio of the vertical change (rise) to the horizontal change (run) between any two points. • (x2, y2) • (x1, y1)

  14. EX Find the slope of the line. (x1, y1) (-5, 4) (x2, y2) (0, 2) (-5, 4) (0, 2)

  15. EX Find the slope of the line. (x1, y1) (-3, 0) (x2, y2) (4, 5) (4, 5) (-3, 0)

  16. EX Find the slope of the line that passes through (3, 5) and ( 6, -1). (x1, y1) (3, 5) (x2, y2) (6, -1)

  17. EX Find the slope of the line that passes through (-2, 4) and ( 4, 4). (x1, y1) (-2, 4) (x2, y2) (4, 4)

  18. EX Find the slope of the line that passes through (3, 5) and (3, 1). (x1, y1) (3, 5) (x2, y2) (3, 1)

  19. Slopes are opposite reciprocals.

  20. EX Given the set of points, determine if are parallel, perpendicular, or neither. A(-2, -2) B (1, 2) C(-3, 6) D(5, 0) The slopes are opposite reciprocals, so they are perpendicular.

  21. Find the slope of the line that contains each pair of points. 1.A(–2, 2), B(4, –2) 2.P(3, 0), X(0, –5) 3.R(–3, –4), S(5, –4) 4.K(–3, 3), T(–3, 1) 5.C(0, 1), D(3, 3) 6.E(–1, 4), F(3, –2) 7.G(–8, –9), H(–3, –5) 8.L(7, –10), M(1, –4)

  22. 4-6 Equations of Lines Objective: Write and graph equations of lines.

  23. Linear Equation

  24. y = 0x + 3 slope y-intercept slope y-intercept

  25. -2x -2x -3y = -2x + 18 -3 -3 -3 slope y-intercept

  26. Step 2: Use the y-intercept and the slope to plot two points and draw the line containing them. –6x + 3y = 12 3y = 6x + 12 Add 6x to each side. = + Divide each side by 3. y = 2x + 4 3y 3 6x 3 12 3 EX Transform the equation –6x + 3y = 12 to slope-intercept form, then graph the resulting equation. Step 1: Transform the equation to slope-intercept form. The slope is 2and the y-intercept is 4.

  27. EX Write an equation of the line that passes through the point (-1, 3) and has a slope of -4. y = mx + b (-1, 3) ( x, y) -4 -4 m = -4 b = -1 y = mx + b y = -4x - 1

  28. EX Write an equation of the line that passes through the point (-3, 0) and has a slope of 1/3. y = mx + b (-3, 0) ( x, y) +1 +1 m = 1/3 b = 1 y = mx + b

  29. EX Write an equation of the line through (-2, 5) and (4, 8). (x1, y1) (-2, 5) (x2, y2) (4, 8) y = mx + b y = mx + b (-2, 5) ( x, y)

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