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October 21, 2016
How to Prove Lines are Parallel
Mathematics is the gate and key to the sciences.
- Roger Bacon
Unit 3, Lesson 4
Postulate 11
If two lines are cut by a transversal and corresponding angles are congruent,then the lines are parallel.
October 21, 2016
Comparing postulate 10 to postulate 11, what do you notice?
Postulate 10If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Postulate 11If two lines are cut by a transversal and corresponding angles are congruent,then the lines are parallel.
We can rewrite postulates 10 and 11 into a single statement....
October 21, 2016
What else could show lines must be parallel?
Theorem 3-5 If two lines are cut by a transversal and alternate interior angles are congruent,then the lines are parallel.
October 21, 2016
Notice that this is the converse of Theorem 3-2.We can rewrite them as the Alternate Interior Angle Theorem
Two lines cut by a transversal are parallel if and only if alternate interior angles are congruent.
Theorem 3-6 If two lines are cut by a transversal and same-side interior angles aresupplementary, then the lines are parallel.
Biconditional
October 21, 2016
You can add these to your theorem list book.
Can we also write the Alternate Exterior Angle Theorem and Same-Side Exterior Angle Theorem as biconditionals?
Theorem 3-7In a plane two lines perpendicular to the same line are parallel.
**Remember Skew lines**
October 21, 2016
Theorem 3-10Two lines parallel to a third line are parallel to each other.
What property does this seem reminiscent of?
We can call this theorem - ________________ of Parallel Lines.
Theorem 3-8
Through a point outside a line there is exactly one line parallel to the given line.
****Not really a Theorem. This should be a postulate*****
October 21, 2016
Theorem 3-9
Through a point outside a line, there is exactlyone line perpendicular to the given line.
Example 1: State which segments (if any) are parallel? State the postulate or theorem.
October 21, 2016
Example 2:
Example 3: Find the value of x and y to make
October 21, 2016
What are all the ways to show two lines are parallel?
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