October 21, 2016

Unit 3, Lesson 4 How to Prove Lines are Parallel Mathematics is the gate and key to the sciences.

- Roger Bacon

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 10 If two parallel lines are cut by a transversal, then corresponding angles are congruent. Postulate 11

If 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 are supplementary, then the lines are parallel.

Biconditional October 21, 2016

Can we also write the Alternate Exterior Angle Theorem and Same-Side Exterior Angle Theorem as biconditionals?

You can add these to your theorem list book.

Theorem 3-7 **Remember Skew lines** In a plane two lines perpendicular to the same line are parallel. October 21, 2016 Theorem 3-10 Two 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 ****Not really a Theorem. This should be a postulate*****

Through a point outside a line there is exactly one line parallel to the given line. October 21, 2016 Theorem 3-9

Through a point outside a line, there is exactly one 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?