View by Category

Loading...

PPT – 3'4 Proving Lines are Parallel PowerPoint presentation | free to view - id: 274adc-MThmZ

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

3.4 Proving Lines are Parallel

- After Quiz, Copy Postulate 16 and Theorems 3.8,

3.9 and 3.10 into your notes. - (Page 150)

Objectives

- Prove that two lines are parallel.
- Use properties of parallel lines to solve

real-life problems.

Postulate 16 Corresponding Angles Converse

- If two lines are cut by a transversal so that

corresponding angles are congruent, then the

lines are parallel.

Theorem 3.8 Alternate Interior Angles Converse

- If two lines are cut by a transversal so that

alternate interior angles are congruent, then the

lines are parallel.

Theorem 3.9 Consecutive Interior Angles Converse

- If two lines are cut by a transversal so that

consecutive interior angles are supplementary,

then the lines are parallel.

Theorem 3.10 Alternate Exterior Angles Converse

- If two lines are cut by a transversal so that

alternate exterior angles are congruent, then the

lines are parallel.

Example 1

- Can you prove that lines p and q are parallel? If

so, describe how.

A.

p

p

p

p

p

p

q

q

q

q

q

q

q

q

p

B.

p

q

q

q

- Can you prove that lines p and q are parallel? If

so, describe how.

C.

p

62

62

q

105

p

D.

105

q

Example 1

- Solutions
- A Yes, Alternate Exterior Angles Converse.
- B No
- C Yes, Alternate Interior Angles Converse.
- D Yes, Corresponding Angles Converse.

Example 2Find the value of x that makes j k.

j

k

x?

4x?

- Solution
- Lines j and k will be parallel if the marked

angles are supplementary. - x? 4x? 180 ?
- 5x 180 ?
- X 36 ?
- So, if x 36, then j k.

Example 3 Using Parallel ConversesUsing

Corresponding Angles Converse

- SAILING. If two boats sail at a 45? angle to the

wind as shown, and the wind is constant, will

their paths ever cross? Explain

Solution

- Because corresponding angles are congruent, the

boats paths are parallel. Parallel lines do not

intersect, so the boats paths will not cross.

Example 4 Identifying parallel lines

- Decide which rays are parallel.

H

E

G

61?

58?

62?

59?

C

A

B

D

A. Is EB parallel to HD? B. Is EA parallel to

HC?

Example 4 Identifying parallel lines

- Decide which rays are parallel.

H

E

G

61?

58?

B

D

- Is EB parallel to HD?
- m?BEH 58?
- m ?DHG 61? The angles are corresponding, but

not congruent, so EB and HD are not parallel.

Example 5 Identifying parallel lines

- Decide which rays are parallel.

H

E

G

120?

120?

C

A

- B. Is EA parallel to HC?
- m ?AEH 62? 58?
- m ?CHG 59? 61?
- ?AEH and ?CHG are congruent corresponding angles,

so EA HC.

Conclusion

- Two lines are cut by a transversal. How can you

prove the lines are parallel? - Show that either a pair of alternate interior

angles, or a pair of corresponding angles, or a

pair of alternate exterior angles is congruent,

or show that a pair of consecutive interior

angles is supplementary.

HW ASSIGNMENT

- 3.4--pp. 153-154 1-25
- Quiz after section 3.5

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "3'4 Proving Lines are Parallel" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!