View by Category

The presentation will start after a short

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

Loading...

PPT – Triangle Inequalities PowerPoint presentation | free to view

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

- 4.6
- Apply inequalities in one triangle.

The positions of the longest and shortest sides

of a triangle are related to the positions of the

largest and smallest angles.

Example 1 Ordering Triangle Side Lengths and

Angle Measures

Write the angles in order from smallest to

largest.

The angles from smallest to largest are ?F, ?H

and ?G.

Example 2 Ordering Triangle Side Lengths and

Angle Measures

Write the sides in order from shortest to longest.

m?R 180 (60 72) 48

A triangle is formed by three segments, but not

every set of three segments can form a triangle.

A certain relationship must exist among the

lengths of three segments in order for them to

form a triangle.

Example 3 Applying the Triangle Inequality

Theorem

Tell whether a triangle can have sides with the

given lengths. Explain.

8, 13, 21

7, 10, 19

Noby the Triangle Inequality Theorem, a triangle

cannot have these side lengths.

Example 4 Applying the Triangle Inequality

Theorem

Tell whether a triangle can have sides with the

given lengths. Explain.

2.3, 3.1, 4.6

?

?

?

Yesthe sum of each pair of lengths is greater

than the third length.

Example 5 Applying the Triangle Inequality

Theorem

Tell whether a triangle can have sides with the

given lengths. Explain.

n 6, n2 1, 3n, when n 4.

Step 1 Evaluate each expression when n 4.

n 6

n2 1

3n

4 6

(4)2 1

3(4)

10

15

12

Example 5 Continued

Step 2 Compare the lengths.

?

?

?

Yesthe sum of each pair of lengths is greater

than the third length.

Example 6 Finding Side Lengths

The lengths of two sides of a triangle are 8

inches and 13 inches. Find the range of possible

lengths for the third side.

Let x represent the length of the third side.

Then apply the Triangle Inequality Theorem.

x 8 gt 13

x 13 gt 8

8 13 gt x

x gt 5

x gt 5

21 gt x

Combine the inequalities. So 5 lt x lt 21. The

length of the third side is greater than 5 inches

and less than 21 inches.

Example 5 Travel Application

The figure shows the approximate distances

between cities in California. What is the range

of distances from San Francisco to Oakland?

Let x be the distance from San Francisco to

Oakland.

x 46 gt 51

x 51 gt 46

46 51 gt x

? Inequal. Thm.

x gt 5

x gt 5

97 gt x

Subtr. Prop. of Inequal.

5 lt x lt 97

Combine the inequalities.

The distance from San Francisco to Oakland is

greater than 5 miles and less than 97 miles.

Check It Out! Example 5

The distance from San Marcos to Johnson City is

50 miles, and the distance from Seguin to San

Marcos is 22 miles. What is the range of

distances from Seguin to Johnson City?

Let x be the distance from Seguin to Johnson

City.

x 22 gt 50

x 50 gt 22

22 50 gt x

? Inequal. Thm.

x gt 28

x gt 28

72 gt x

Subtr. Prop. of Inequal.

28 lt x lt 72

Combine the inequalities.

The distance from Seguin to Johnson City is

greater than 28 miles and less than 72 miles.

Homework

- Pg 216 1-20
- Extra help and problems are on the next slides.

Go to my website to see them.

Lesson Quiz Part I

1. Write the angles in order from smallest to

largest. 2. Write the sides in order from

shortest to longest.

?C, ?B, ?A

Lesson Quiz Part II

3. The lengths of two sides of a triangle are 17

cm and 12 cm. Find the range of possible lengths

for the third side. 4. Tell whether a triangle

can have sides with lengths 2.7, 3.5, and 9.8.

Explain.

5 cm lt x lt 29 cm

No 2.7 3.5 is not greater than 9.8.

5. Ray wants to place a chair so it is 10 ft from

his television set. Can the other two

distances shown be 8 ft and 6 ft? Explain.

Yes the sum of any two lengths is greater than

the third length.

Check It Out! Example 1

Write the angles in order from smallest to

largest.

The angles from smallest to largest are ?B, ?A,

and ?C.

Check It Out! Example 2

Write the sides in order from shortest to longest.

m?E 180 (90 22) 68

Check It Out! Example 3

The lengths of two sides of a triangle are 22

inches and 17 inches. Find the range of possible

lengths for the third side.

Let x represent the length of the third side.

Then apply the Triangle Inequality Theorem.

x 22 gt 17

x 17 gt 22

22 17 gt x

x gt 5

x gt 5

39 gt x

Combine the inequalities. So 5 lt x lt 39. The

length of the third side is greater than 5 inches

and less than 39 inches.

Example

- A landscape architect is designing a triangular

deck. She wants to place benches in the two

largest corners. In which corners should she

place the benches?

27ft

?

21ft

19ft

Homework

- P. 216 1-24

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

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 2015 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2015 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!