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Geometry 3.4

Geometry 3.4. Perpendicular Lines. Learning Targets. Students should be able to… Prove and apply theorems about perpendicular lines. Warm-up. 1. Name the line that is the transversal. 2. Name the parallel lines. 3. Name all the pairs of Corresponding Angles.

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Geometry 3.4

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  1. Geometry 3.4 Perpendicular Lines

  2. Learning Targets • Students should be able to… • Prove and apply theorems about perpendicular lines.

  3. Warm-up 1. Name the line that is the transversal. 2. Name the parallel lines. 3. Name all the pairs of Corresponding Angles. 4. Name all the pairs of Alternate Interior Angles. 5. Name all the pairs of Alternate Exterior Angles. 6. Name all pairs of Consecutive Interior Angles. 7. Name all pairs of Consecutive Exterior Angles. 8. Name all pairs of Vertical Angles.

  4. Go over Quiz

  5. Vocabulary l M A B

  6. Vocabulary l M A B P B A C

  7. Construction of a perpendicular Bisector of a segment • Draw . • Open the compass wider than half of AB and draw an arc centered at A • Using the same compass setting draw an arc centered at B that intersects the first arc at C and D • Draw C A B is the perpendicular bisector of D

  8. Section 3-4 Postulates & Theorems • POSTULATE: Parallel Postulate: If a point is not on a line, then there is 1 line that can be drawn through it so that it is parallel to the first line.

  9. Section 3-4 Postulates & Theorems • POSTULATE - Perpendicular Postulate: If a point is not on a line, then there is 1 line that can be drawn through it so that it is perpendicular to the first line.

  10. Section 3-4 Postulates & Theorems • Theorem: If 2 lines are parallel to the same line, they are parallel to each other.

  11. Section 3-4 Postulates & Theorems • Theorem 3-4-1: If 2 intersecting lines form a linear pair of congruent angles, then the lines are perpendicular.

  12. Section 3-4 Postulates & Theorems • Theorem 3-4-2: If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

  13. Section 3-4 Postulates & Theorems • Theorem 3-4-3: If 2 lines are perpendicular to the same line, then they are parallel to each other.

  14. Practice Problems

  15. Practice Problems 4 8 90º

  16. Practice Problems

  17. Practice Problems 5

  18. Practice Problems , x > 8 , x < 23

  19. Practice Problems , x +5 < 9, x < 9

  20. Practice Problems , x + 5 > 9, x > 11

  21. Practice Problems , x > 7 , x < 3.5 , x > 9 , x < 17

  22. Practice Problems D

  23. Practice Problems

  24. Practice Problems

  25. Homework • Page 174 – 175 #2, 3, 6, 7, 10 – 15

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