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Section 3.1 Lines and Angles

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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