Triangle Inequality Theorem

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

Bisecting an Angle

Example of the types of problems you will encounter.

Multiple Choice

Angle LMN is bisected by ray MP. The measure of <LMP is 62 degrees. What is the m<NMP? (Draw it out on scratch paper!)

• $118\degree$

• $31\degree$
  

• $28\degree$

Multiple Choice

Angle ABC is bisected by ray BD. The measure of <ABD is 23 degrees. What is the m<ABC? (Draw it out on scratch paper!)

•  $46\degree$  
  

•  $67\degree$  
  

•  $157\degree$