Chapter 3 Theorems and Postulates

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Author:
ashleycortes
ID:
218480
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Chapter 3 Theorems and Postulates
Updated:
2013-05-08 00:57:51
Tags:
math geometry nunes theorems postulates three
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Homework Check on Wednesday, 8 May 2013.
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  1. If 2 parallel planes are cut by a third plane, then the lines of intersection are parallel.
    Theorem 3-1
  2. If 2 parallel lines are cut by a transversal, then corresponding angles are congruent.
    Postulate 10
  3. If 2 parallel lines are cut by a transversal, then alternate interior angles are congruent.
    Theorem 3-2
  4. If 2 parallel lines are cut by a transversal, then same-side interior angles are supplementary.
    Theorem 3-3
  5. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.
    Theorem 3-4
  6. If 2 lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
    Postulate 11
  7. If 2 lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.
    Theorem 3-5
  8. If 2 lines are cut by a transversal and same-side interior angels are supplementary, then the lines are parallel.
    Theorem 3-6
  9. In a plane, 2 lines perpendicular to the same line are parallel.
    Theorem 3-7
  10. Through a point outside a line, there is exactly 1 line parallel to the given line.
    Theorem 3-8
  11. Through a point outside a line, there is exactly 1 line perpendicular to the given line.
    Theorem 3-9
  12. 2 lines parallel to a third line are parallel to each other.
    Theorem 3-10
  13. Name 5 ways to prove two lines are parallel when all three lines are coplanar.
    • Show that a pair of corresponding angles are congruent.
    • Show that a pair of alternate interior angles are congruent.
    • Show that a pair of same-side interior angles are supplementary.
    • In a plane show that both lines are perpendicular to a third line.
    • Show that both lines are parallel to a third line.

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