Triangle Inequality Theorem and Triangle Sum

Triangle Inequality Theorem

Can we make a triangle?

Notice the greater than symbol! It is NOT the greater than or equal to symbol.

Why do I need to know this?

• Sometimes you will NOT be given a picture and you have to determine if you can create a triangle given the number lengths provided.

• Example: Given the lengths 2, 5, and 8cm, can you create a triangle?

What if the sum equals the other side?

• Ex: 2, 5, 7 are given and if you add 2 + 5 you get 7.... 7 is not greater than 7, so you CANNOT create a triangle.

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Example of proving a triangle can be made with the given side lengths of 7, 8, and 9.

Example of proving a triangle cannot be made with the given side lengths of 4, 8, and 2.

Multiple Choice

Can the following side measures form a triangle?

3, 5, 8

• Yes

• No

Multiple Choice

Can the sides of a triangle have lengths 4, 7, and 18?

• Yes

• No

Multiple Choice

Can the sides of a triangle have lengths 4, 11, and 13?

• Yes

• No

Multiple Choice

Determine if it is possible to form a triangle with the given side lengths. 6 yd, 8 yd, 9 yd

• yes

• no

Multiple Choice

Will these line segments form a triangle?

• yes

• no

Multiple Choice

Select the measurements that match the sides of a triangle (there is only one that will make a triangle!)

• 7, 9, 19

• 7, 12, 1

• 7, 7, 7

• 7, 7, 16

Multiple Choice

Does a triangle with these side lengths exist?

15, 12, 9

• Yes

• No

Multiple Choice

9. Which of these lengths CANNOT represent the sides of a triangle?

• 32, 34, 60

• 28, 30, 58

• 13, 20, 27

• 2, 4, 5

Multiple Choice

Can these sides form a triangle? 2, 9, 5

• Yes

• No

Multiple Choice

State if the three numbers can be the measures of the sides of a triangle: 8, 19, 11

• no

• yes

• not enough information

Multiple Choice

Can these sides form a triangle? 6, 4, 4

• Yes

• No

Multiple Select

Which of the following could be the third side of a triangle with sides 5.2 and 7.2? Check all that apply.

• 21

• 2

• 9

• 12.4

• 11

Multiple Select

Which of the following could NOT be the third side of a triangle with sides 35 and 14? Check all that apply.

• 21

• 48

• 26

• 35

• 14

Multiple Choice

If the measures of 2 sides of a triangle are 57 and 32, what is the LEAST possible measure of the third side if the measure is an integer?

• 25

• 26

• 88

• 89

Multiple Choice

Determine if it is possible to form a triangle with the given side lengths. 7 yd, 8 yd, 9 yd

• yes
• no

Multiple Choice

Identify the longest side measure.

• AC
• BA
• BC

Multiple Choice

Will these three sides form a triangle?

• yes

• no

Multiple Choice

Will these line segments form a triangle?

• yes

• no

Multiple Choice

Which set of side lengths will form a triangle?

• 3, 6, 12

• 7, 7, 14

• 9, 9, 9

• 13, 6, 7

Multiple Choice

Identify the smallest angle.

• ∠K
• ∠L
• ∠M

Multiple Choice

9. Which of these lengths CANNOT represent the sides of a triangle?

• 32, 34, 60
• 28, 30, 58
• 13, 20, 27
• 2, 4, 5

Multiple Choice

Can the following side measures form a triangle?
  3 ft, 5 ft, 8 ft 

• Yes
• No

Multiple Choice

1.  What is the longest side in ∆GOD?

• $$\overline{DO}$$   

• $$\overline{GD}$$  

•    $$\overline{GO}$$  

• $$\overline{DG}$$  

Multiple Choice

2. What is the shortest side in ∆GOD?

• $$\overline{DO}$$   

• $$\overline{GD}$$  

• $$\overline{OG\ }$$   

• $$\overline{DG}$$  

Multiple Choice

$$Find\ the\ measure\ of\ \angle\ k.\ Then\ name\ the\ triangle\ based\ on\ it's\ angle.\$$  

• $$60\degree\ ;\ obtuse\ triangle\$$  

• $$60\degree\degree\ ;\ equangular\ triangle\$$  

• $$80\degree\ ;\ equaingular\ triangle$$   

• $$80\degree\ ;\ acute\ triangle\$$  

Multiple Choice

How many pennies equal 1 dollar?

• 1,000

• 100

• 10

• 100,000,000

Multiple Choice

Which is an even number?

• 88

• 63

• 21

• 17