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Chapter 3

Chapter 3. Section 3.1 & 3.2 Identify pairs of lines and angles and use parallel lines with transversals. Objective: SWBAT identify angle pairs formed by three intersecting lines, and use angles formed by parallel lines and transversals. Parallel Lines. Lines that do not Intersect

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Chapter 3

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  1. Chapter 3 Section 3.1 & 3.2 Identify pairs of lines and angles and use parallel lines with transversals Objective: SWBAT identify angle pairs formed by three intersecting lines, and use angles formed by parallel lines and transversals.

  2. Parallel Lines Lines that do not Intersect and are coplanar

  3. Parallel Planes Planes that Do not Intersect

  4. Skew Lines Lines that do Not intersect and are not Coplanar.

  5. Ex. 1: Identify Relationships in Space • Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description?

  6. Some More Postulates • Parallel Postulate: • If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.

  7. Some More Postulates • Perpendicular Postulate • If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

  8. Transversal a line that intersects two or more coplanar lines at different points.

  9. Vocabulary 4 types of angles formed by a transversal:

  10. Vocabulary

  11. Classify the angle pair x y

  12. Classify the angle pair m n

  13. Classify the angle pair p q

  14. More Postulates and Theorems • Corresponding Angles Postulate • If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent

  15. More Postulates and Theorems • Alternate Interior Angles Theorem • If two parallel lines are cut by a transversal, then the pairs of alternate interior angles and congruent.

  16. More Postulates and Theorems • Alternate Exterior Angles Theorem • If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

  17. More Postulates and Theorems • Consecutive Interior Angles Theorem • If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

  18. Solve for the variable 2p 120

  19. Solve for the variable x 80

  20. Find all the missing angle measures 105

  21. Solve for x and the measure of angle 4.

  22. Use the diagram. If m 3 = 68° and m 8 = (2x + 4)°, what is the value of x? Show your steps. Example:

  23. Homework • Textbook pg. 142 • # 4, 6, 18, 20, 22 • Textbook pg. 149 • # 4, 6, 8, 17, 19

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