1. 3-3: Proving Lines Parallel
PIB Geometry
3-3: Proving Lines Parallel

2. 3-2 Homework Questions?
Just so we’re clear, you absolutely cannot use Theorem 3-3 as a reason in your proof for #22.

3. 3-3 Objectives
Determine when we can conclude lines cut by a transversal are parallel.
State and apply other theorems about parallels and perpendiculars.

4. 3-3 Theorems/Postulates are converses of the ones we learned yesterday:
Postulate 11: CP Postulate Theorem 3-5: AIP Theorem Theorem 3-6: SSIP Theorem

5. 3-3 Self-Guided Notes
Use p in your textbook to complete the self-guided notes on your own or with a partner.

6. Example – Drawing auxiliary lines
What is 𝑚∠𝑅𝑆𝑇?

7. Some historical context
Euclid’s only 5 postulates:
A line can be drawn containing any two points.
Any line segment can be extended into a line.
Given any line segment, a circle can be drawn having the segment as its radius and one endpoint as the center.
All right angles are congruent.
(The Parallel Postulate) Given a line and point not on that line, there exists one and only one line which passes through the point and is parallel to the line.

8. To summarize, we have 5 ways to prove lines are parallel:
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
Show that both lines are parallel to a third line
In a plane, show that both lines are perpendicular to a third line.