# Chapter 3 Theorems and Postulates

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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.
 Author: ashleycortes ID: 218480 Card Set: Chapter 3 Theorems and Postulates Updated: 2013-05-08 04:57:51 Tags: math geometry nunes theorems postulates three Folders: Description: Homework Check on Wednesday, 8 May 2013. Show Answers: