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Advanced Geometry Ch 4: Lines in the Plane

Advanced Geometry Ch 4: Lines in the Plane. 4.5 Introduction to Parallel Lines. Lesson Objectives. After studying this section, students will be able to:. Recognize planes Recognize transversals Identify the pairs of angles formed by transversal lines

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Advanced Geometry Ch 4: Lines in the Plane

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  1. Advanced GeometryCh 4: Lines in the Plane 4.5 Introduction to Parallel Lines

  2. Lesson Objectives After studying this section, students will be able to: • Recognize planes • Recognize transversals • Identify the pairs of angles formed by • transversal lines • Recognize parallel lines

  3. Definition: A planeis a surface such that if any two points on the surface are connected by a line, all points of the line are also on the plane. A PLANE HAS: Two dimensions: they are length and width  WIDTH  Infinite length and width NO THICKNESS, So a plane does not have height or depth . . .  L E N G T H 

  4. I have a surface, that means I am A PLANE, TOO! Do you know what dimension(s) determine my “length” and “width”? COORDINATE PLANE “PLAIN” PLANE

  5. t 5 6 1 2 4 3 8 7 Which angles are congruent? (These must have the same measure) Which angles are supplementary? (These have a sum of 180⁰!) What is a Theorem that could easily be applied in this situation? (Starts with a V!)

  6. 5 6 4 7 8 3 2 t 1 Parallel Lines & Transversals List all pairs of angles that fit the description. • Corresponding • Alternate Interior • Alternate Exterior • Consecutive Interior

  7. Corresponding Angles 4 and 2 3 and 1 5 and 7 6 and 8 5 6 4 7 8 3 2 t 1

  8. Alternate Interior Angles 3 and 7 2 and 6 5 6 4 7 8 3 2 t 1

  9. Alternate Exterior Angles 5 and 1 4 and 8 5 6 4 7 8 3 2 t 1

  10. Consecutive Interior 5 3 and 2 6 and 7 6 4 7 8 3 2 t 1

  11. Find all angle measures t 180 - 67 113  67  1 3 67  2 113  113  5 67  8 67  6 7 113 

  12. Equations Part II

  13. Alternate Exterior Angles • Name the angle relationship • Are they congruent or supplementary? • Find the value of x  t 5x = 125 125  5 5 x = 25 5x 

  14. Corresponding Angles • Name the angle relationship • Are they congruent or supplementary? • Find the value of x  t 2x + 1 = 151 - 1 - 1 2x + 1 2x = 150 2 2 151 x = 75

  15. Consecutive Interior Angles • Name the angle relationship • Are they congruent or supplementary? • Find the value of x supp t 7x + 15 + 81 = 180 7x + 96 = 180 - 96 - 96 81 7x = 84 7x + 15 7 7 x = 12

  16. Alternate Interior Angles • Name the angle relationship • Are they congruent or supplementary? • Find the value of x  t 2x + 20 = 3x - 2x - 2x 3x 20 = x 2x + 20

  17. 4.5 Homework Pp. 197 – 198 #’s 1 – 5

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