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Section 3.1 Lines and Angles

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Section 3.1 Lines and Angles. Perpendicular Lines. Intersecting lines that form right angles Symbol. XS SR. Parallel Lines. Two lines that are coplanar and do not intersect Symbol: II. XY II UZ. Skew Lines. Lines do not intersect and are not coplanar. Example.

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Section 3.1 Lines and Angles

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  1. Section 3.1 Lines and Angles

  2. Perpendicular Lines • Intersecting lines that form right angles • Symbol XS SR

  3. Parallel Lines • Two lines that are coplanar and do not intersect • Symbol: II XY II UZ

  4. Skew Lines • Lines do not intersect and are not coplanar

  5. Example • Is XY parallel or skew to RV? XY II RV

  6. Parallel planes • Two planes that do not intersect

  7. 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.

  8. 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.

  9. D A B C Theorem 3.1 • If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular • Ex 1 m<ABD = m<DBC and a linear pair, BD AC

  10. F J G H Theorem 3.2 • If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. • Ex. 2 <FGJ is complementary to <JGH

  11. Examples: Solve for x Ex 3. x 60° ANSWER: 60 + x = 90 -60 -60 x = 30

  12. x 55° Example 4 ANSWER: x + 55 = 90 -55 -55 x = 35

  13. 27° (2x-9)° Example 5 ANSWER: 2x – 9 + 27 = 90 2x +18 = 90 2x = 72 x = 36

  14. Theorem 3.3 • If 2 lines are perpendicular, then they intersect to form four right angles. l m

  15. Complete Try it! Problems #1-8

  16. Transversal • A line that intersects two or more coplanar lines at different points. transversal

  17. 1 2 3 4 6 5 7 8 Vertical Angles • Formed by the intersection of two pairs of opposite rays

  18. 1 2 3 4 6 5 7 8 Linear Pair • Adjacent angles that are supplementary

  19. 1 2 3 4 6 5 7 8 Corresponding Angles • Occupy corresponding positions.

  20. 1 2 3 4 6 5 7 8 Alternate Exterior Angles • Lie outside the 2 lines on opposite sides of the transversal.

  21. 1 2 3 4 6 5 7 8 Alternate Interior Angles • Lie between the 2 lines on opposite sides of the transversal.

  22. 1 2 3 4 6 5 7 8 Consecutive Interior Angles(Same side interior angles) • Lie between the 2 lines on the same side of the transversal.

  23. 1 2 3 4 5 6 8 7 Angle Relationships: Name a pair of angles • Corresponding • Ex. 1 & 5 • Alternate Exterior • Ex. 2 & 7 • Alternate Interior • Ex. 4 & 5 • Consecutive Interior • Ex. 3 & 5

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