View by Category

Loading...

PPT – Triangle Inequalities PowerPoint presentation | free to download - id: 9fc69-ZTM2Z

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Triangle Inequalities

- 7.1 Segments, Angles, and Inequalities

- 7.2 Exterior Angle Theorem

- 7.3 Inequalities Within a Triangle

- 7.4 Triangle Inequality Theorem

Inequalities

Segments, Angles, and Inequalities

What You'll Learn

You will learn to apply inequalities to segment

and angle measures.

1) Inequality

Segments, Angles, and Inequalities

The Comparison Property of Numbers is used to

compare two line segments ofunequal measures.

The property states that given two unequal

numbers a and b, either

a gt b

a lt b or

The same property is also used to compare angles

of unequal measures.

Segments, Angles, and Inequalities

The measure of ?J is greater than the measure of

?K.

inequalities

The statements TU gt VW and ?J gt ?K are called

__________ becausethey contain the symbol lt or

gt.

a lt b

a b

a gt b

Segments, Angles, and Inequalities

gt

SN

DN

6 (- 1)

6 2

gt

7

4

Segments, Angles, and Inequalities

AB gt CB

AB gt AC

A similar theorem for comparing angle measures is

stated below.This theorem is based on the Angle

Addition Postulate.

Segments, Angles, and Inequalities

A similar theorem for comparing angle measures is

stated below.This theorem is based on the Angle

Addition Postulate.

Segments, Angles, and Inequalities

Use theorem 7 2 to solve the following problem.

lt

m?BDA

m?CDA

45

40 45

lt

45

85

Segments, Angles, and Inequalities

For any numbers a, b, and c,

if 5 lt 8 and 8 lt 9, then 5 lt 9.

1) if a lt b and b lt c, then a lt c.

2) if a gt b and b gt c, then a gt c.

if 7 gt 6 and 6 gt 3, then 7 gt 3.

Segments, Angles, and Inequalities

For any numbers a, b, and c,

1) if a lt b, then a c lt b c and a c

lt b c.

1 lt 3 1 5 lt 3 5 6 lt 8

2) if a gt b, then a c gt b c and a c

gt b c.

For any numbers a, b, and c,

End of Section 7.1

Exterior Angle Theorem

What You'll Learn

You will learn to identify exterior angles and

remote interior angles of a triangle and use the

Exterior Angle Theorem.

1) Interior angle 2) Exterior angle 3) Remote

interior angle

Exterior Angle Theorem

interior

In the triangle below, recall that ?1, ?2, and ?3

are _______ angles of?PQR.

exterior

Angle 4 is called an _______ angle of ?PQR.

An exterior angle of a triangle is an angle that

forms a _________ with one of the angles of the

triangle.

linear pair

In ?PQR, ?4 is an exterior angle at R because it

forms a linear pair with ?3.

Remote interior angles

____________________ of a triangle are the two

angles that do not form a linear pair with the

exterior angle.

In ?PQR, ?1, and ?2 are the remote interior

angles with respect to ?4.

Exterior Angle Theorem

In the figure below, ?2 and ?3 are remote

interior angles with respect to what angle?

?5

Exterior Angle Theorem

remote interior angles

m?4

m?1 m?2

Exterior Angle Theorem

Exterior Angle Theorem

remote interior angles

m?4 gt

m?1

m?4 gt

m?2

Exterior Angle Theorem

Name two angles in the triangle below that have

measures less than 74.

?1 and ?3

acute

Exterior Angle Theorem

Exterior Angle Theorem

The feathershaped leaf is called a

pinnatifid. In the figure, does x y?

Explain.

28

__ 81 32 78

28

109 110

No! x does not equal y

End of Section 7.2

Inequalities Within a Triangle

What You'll Learn

You will learn to identify the relationships

between the _____ and _____ of a triangle.

sides

angles

Nothing New!

Inequalities Within a Triangle

in the same order

LP lt

PM lt

ML

m?M lt

m?P

m?L lt

Inequalities Within a Triangle

in the same order

m?W lt

m?K

m?J lt

JK lt

KW lt

WJ

Inequalities Within a Triangle

greatest measure

5

3

4

WY gt

XW

WY gt

XY

Inequalities Within a Triangle

The longest side is

The largest angle is

So, the largest angle is

So, the longest side is

End of Section 7.3

Triangle Inequality Theorem

What You'll Learn

You will learn to identify and use the Triangle

Inequality Theorem.

Nothing New!

Triangle Inequality Theorem

greater

a b gt c

a c gt b

b c gt a

Triangle Inequality Theorem

Can 16, 10, and 5 be the measures of the sides of

a triangle?

16 10 gt 5

No!

16 5 gt 10

End of Section 7.4

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

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

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: "Triangle Inequalities" 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!