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If parallel lines lie in two distinct planes, the planes must be parallel.

If parallel lines lie in two distinct planes, the planes must be parallel. FALSE. Three planes can intersect at a point. TRUE (ex: corner of classroom). Three planes can intersect at a line. TRUE. If two lines in space are not parallel, then they must intersect. FALSE (Skew lines).

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If parallel lines lie in two distinct planes, the planes must be parallel.

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  1. If parallel lines lie in two distinct planes, the planes must be parallel.

  2. FALSE

  3. Three planes can intersect at a point.

  4. TRUE (ex: corner of classroom)

  5. Three planes can intersect at a line.

  6. TRUE

  7. If two lines in space are not parallel, then they must intersect.

  8. FALSE (Skew lines)

  9. If lines are perpendicular to the same plane, they are parallel.

  10. TRUE

  11. If a line is perpendicular to a line in a plane, then it is perpendicular to the plane.

  12. FALSE (Mailbox problem… must be perp. to two lines in plane passing through foot)

  13. If a line is perpendicular to one of two parallel planes, then it is perpendicular to the other.

  14. TRUE

  15. If a line is perpendicular to a plane, then it is perpendicular to all lines in the plane.

  16. FALSE (Not perp. to lines not passing through its foot)

  17. If separate planes contain skew lines, the planes are parallel.

  18. FALSE

  19. Two planes can intersect at a point.

  20. FALSE (planes continue infinitely)

  21. Two planes can intersect at a line.

  22. TRUE (crack at top of classroom)

  23. The union of two planes is an angle.

  24. FALSE (an angle is formed by lines – this is called a dihedral angle)

  25. Two intersecting lines can lie in more than one plane.

  26. FALSE (intersecting lines determine a plane)

  27. Two parallel lines determine a plane.

  28. TRUE

  29. Two skew lines determine a plane.

  30. FALSE (by definition, skew lines lie in different planes)

  31. Three points determine a plane.

  32. FALSE (must be non-collinear)

  33. If three lines are parallel, then they must be coplanar.

  34. FALSE

  35. In a plane, if two lines are perpendicular to the same line, they are parallel.

  36. TRUE

  37. In space, if two lines are perpendicular to the same line, they are parallel.

  38. FALSE

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