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5-5

5-5. Coordinate Geometry. Warm Up. Problem of the Day. Lesson Presentation. Course 3. 5-5. Coordinate Geometry. Course 3. Warm Up Complete each sentence. 1 . Two lines in a plane that never meet are called lines. 2 . lines intersect at right angles.

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5-5

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  1. 5-5 Coordinate Geometry Warm Up Problem of the Day Lesson Presentation Course 3

  2. 5-5 Coordinate Geometry Course 3 Warm Up Complete each sentence. 1. Two lines in a plane that never meet are called lines. 2. lines intersect at right angles. 3. The symbol || means that lines are . 4. When a transversal intersects two lines, all of the acute angles are congruent. parallel Perpendicular parallel parallel

  3. 5-5 Coordinate Geometry Course 3 Problem of the Day What type of polygon am I? My opposite angles have equal measure. I do not have a right angle. All my sides are congruent. rhombus

  4. 5-5 Coordinate Geometry Course 3 Learn to identify polygons in the coordinate plane.

  5. 5-5 Coordinate Geometry Course 3 Insert Lesson Title Here Vocabulary slope rise run

  6. 5-5 Coordinate Geometry Course 3 In computer graphics, a coordinate system is used to create images, from simple geometric figures to realistic figures used in movies. Properties of the coordinate plane can be used to find information about figures in the plane, such as whether lines in the plane are parallel.

  7. 5-5 Coordinate Geometry Course 3 Slope is a number that describes how steep a line is.

  8. 5-5 Coordinate Geometry riserun vertical change horizontal change Course 3 = slope = The slope of a horizontal line is 0. The slope of a vertical line is undefined.

  9. 5-5 Coordinate Geometry A. XY positive slope; slope of XY = = 5 4 –5 –4 Course 3 Additional Example 1A: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line.

  10. 5-5 Coordinate Geometry negative slope; slope of ZA = = – –1 2 1 2 Course 3 Additional Example 1B: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B. ZA

  11. 5-5 Coordinate Geometry slope of BC is undefined Course 3 Additional Example 1C: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. C. BC

  12. 5-5 Coordinate Geometry slope of DM = 0 Course 3 Additional Example 1D: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. D. DM

  13. 5-5 Coordinate Geometry A. AB positive slope; slope of AB = 1 8 Course 3 Try This: Example 1A Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B A C E F G H D

  14. 5-5 Coordinate Geometry slope of CD is undefined Course 3 Try This: Example 1B Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B A B. CD C E F G H D

  15. 5-5 Coordinate Geometry slope of EF = 0 Course 3 Try This: Example 1C Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B A C. EF C E F G H D

  16. 5-5 Coordinate Geometry negative slope; slope of GH = = – –1 3 1 3 Course 3 Try This: Example 1D Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B A D. GH C E F G H D

  17. 5-5 Coordinate Geometry Course 3

  18. 5-5 Coordinate Geometry 3 2 slope of EF = 3 5 slope of GH = 3 5 slope of PQ = –2 3 2 3 slope of CD = or – 3 –3 slope of QR = or –1 Course 3 Additional Example 2: Finding Perpendicular Line and Parallel Lines Which lines are parallel? Which lines are perpendicular?

  19. 5-5 Coordinate Geometry GH || PQ 3 5 3 5 The slopes are equal. = EFCD The slopes have a product of –1: • – = –1 2 3 3 2 Course 3 Additional Example 2 Continued Which lines are parallel? Which lines are perpendicular?

  20. 5-5 Coordinate Geometry –4 6 –6 4 –2 3 –3 2 slope of EF = or slope of AB = or –2 3 slope of CD = 2 3 slope of GH = 3 3 slope of JK = or 1 Course 3 Try This: Example 2 Which lines are parallel? Which lines are perpendicular? A C K D E H B J G F

  21. GHAB 5-5 Coordinate Geometry CD || EF –2 3 –2 3 The slopes are equal. = The slopes have a product of –1: • – = –1 3 2 2 3 Course 3 Try This: Example 2 Continued Which lines are parallel? Which lines are perpendicular? A C K D E H B J G F

  22. 5-5 Coordinate Geometry CD || BA and BC || AD Course 3 Additional Example 3A: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(3, –2), B(2, –1), C(4, 3), D(5, 2) parallelogram

  23. 5-5 Coordinate Geometry TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU Course 3 Additional Example 3B: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2) parallelogram, rectangle, rhombus, square

  24. 5-5 Coordinate Geometry GH || JI Course 3 Additional Example 3C: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. C. G(1, –1), H(1, –2), I(3, –3), J(3, 1) trapezoid

  25. 5-5 Coordinate Geometry WZ || XY and WX || ZY WZ^ZY, ZY^XY, XY^WX and WX^WZ Course 3 Additional Example 3D: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. D. W(2, –3), X(3, –4), Y(6, –1), Z(5, 0) parallelogram, rectangle

  26. 5-5 Coordinate Geometry CD || BA and BC || AD Course 3 Try This: Example 3A Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(–1, 3), B(1, 5), C(7, 5), D(5, 3) B C A D parallelogram

  27. 5-5 Coordinate Geometry EF || HG Course 3 Try This: Example 3B Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. E(1, 5), F(7, 5), G(6, 1), H(2, 1) E F trapezoid G H

  28. 5-5 Coordinate Geometry ZW || YX and WX || ZY WX^ZW, XY^WX, YZ^XY and ZW^YZ Course 3 Try This: Example 3C Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. C. W(4, 8), X(8, 2), Y(2, –2), Z(–2, 4) W Z X parallelogram, rectangle, rhombus, square Y

  29. 5-5 Coordinate Geometry TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU Course 3 Try This: Example 3D Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. D. R(–1, 1), S(3, 7), T(6, 5), U(2, –1) S T R parallelogram, rectangle U

  30. 5-5 Coordinate Geometry 10 3 – MN, RQ Course 3 Insert Lesson Title Here Lesson Quiz Determine the slope of each line. 1.PQ 2.MN 3.MQ 4.NP 5. Which pair of lines are parallel? 1 8 7

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