Loading...

PPT – Lesson 3-3: Proving Lines Parallel PowerPoint presentation | free to download - id: 6a2791-OTAyZ

The Adobe Flash plugin is needed to view this content

Lesson 3-3 Proving Lines Parallel

- Todays Learning Goals
- Which theorem proves two lines are parallel?
- How do I set up an equation to solve for the

x-value that will make two lines parallel?

Review

- 1. Solve for x.

- 2. What is a converse to a conditional statement?

Postulate 3-2 Converse of the Corresponding

Angles Postulate

- Corresponding Angles postulate states If lines

cut by a transversal are parallel, then the

corresponding angles are congruent. - Corresponding Angles Converse If lines cut by a

transversal form corresponding angles that are

congruent, then - the lines are parallel.

Example Which lines are parallel? Justify your

answer.

- 1) If ?
- 2) If ?

Converses to the other Angle Theorems

- Alternate Interior Angles Theorem Converse If

alternate interior angles are congruent, then the

lines are parallel. - Alternate Exterior Angles Theorem Converse If

alternate exterior angles are congruent, then the

lines are parallel.

Converses to the other Angle Theorems

- Same-Side Interior Angles Theorem Converse If

same-side interior angles are supplementary, then

the lines are parallel. - Same-Side Exterior Angles Theorem Converse If

same-side exterior angles are supplementary, then

the lines are parallel.

Proof Alternate Interior Angles Converse

- Statements Reasons
- 1. 1.
- 2. 2.
- 3. 3.
- 4. 4.

Given

Vertical Angles Theorem

Transitive Property of

Corresponding Angles Converse

Proof Same-Side Exterior Angles Converse

- Statements Reasons
- 1. 1.
- 2. 2.
- 3. 3.
- 4. 4.

Given

Vertical Angles Theorem

Transitive Property of

Corresponding Angles Converse

Example Are the lines parallel?

- If , are lines r and s parallel?

Justify your answer.

Last Example! Solving for X

- What value of x would make the lines parallel?
- a) b)

Recap Theorems vs Converses

- The angle pair THEOREMS
- Given - lines are parallel
- Conclusion angle pairs are or

supplementary - Angle pair CONVERSES
- Given - angle pairs are or supplementary
- Conclusion lines are parallel

3-3 Classwork

- You may work with a partner, no changing seats.
- Heading
- 3-3 Classwork pg 169 1, 2, 7, 9, 14, 19, 20,

22, 23, 24