4. Practice: Triangle Inequality Theorem

A triangle can have side lengths 6, 8 and 15. (a)  

• True
• False

A triangle can have side lengths 4, 3 and 10. (a)  

• True
• False

A triangle can have side lengths 5.2, 6.3 and 10.5. (a)  

• True
• False

Three students wrote side lengths that they thought would form a triangle.  Which student(s) were correct?

• Keisha

• Miguel

• Ralphie

Use the triangle inequality theorem to prove whether a triangle can have side lengths 6, 8, and 15. Then decide if each part of the triangle inequality theorem is true or false.

6 + ​ 8 > 15 ​​ (a)  

​ (b)   + 15 > ​ 8 ​​ (c)  

8 + ​ (d)   > ​ ​ 6 ​ (e)  

• False
• True
• 8
• 8

Use the triangle inequality theorem to prove whether a triangle can have side lengths 4, 3, and 10. Then decide if each part of the triangle inequality theorem is true or false.

3 + ​ 4 > 10 ​​ (a)  

​ (b)   + 10 > ​ 4 ​ (c)  

10 + ​ (d)   > 3 ​ (e)  

• False
• True

Use the triangle inequality theorem to prove whether a triangle can have side lengths 5.2, 6.3, and 10.5.

5.2 + ​ 6.3 > 10.5 ​​ ​ (a)  

​ (b)   + 10.5 > ​ 6.3 ​ (c)  

10.5 + ​ (d)   > 5.2 ​ (e)  

• True
• False