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

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

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

3-3 Self-Guided Notes Use p. 83-85 in your textbook to complete the self-guided notes on your own or with a partner.

Example – Drawing auxiliary lines What is 𝑚∠𝑅𝑆𝑇?

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.

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.