1. The Concept The Triangle Inequality Theorem states that any two sides of a triangle when added together will always be larger than the third. EX: 6 7 12 6+12=18 (this is bigger than 7) 12+7=19 (this is bigger than 6) 6+7=13 (this is bigger than 12)

2. Lets Practice Do the three sides form a triangle? 1.10, 9, 10 2.12, 27, 12 3.8, 10, 7 4.3, 8, 10 5.11, 9, 23

3. Answers 1. 10, 9, 10YES 2.12, 27, 12NO 3.8, 10, 7YES 4.3, 8, 10YES 5.11, 9, 23NO

4. How to Find the range for a Missing Side What is the definition of Range? To find the range for a missing side you subtract the two numbers to find the lowest possible value and add the numbers to find the highest possible value. EX: 12, 9 Subtract to find the lowest Add to find the Highest X > 3 X < 21 To write this as one statement we would say 3 < x < 21 This means that my missing side must be greater than 3 but less than 21

5. Practice Give the range for the missing side as one statement. 1.9, 7 2.12, 9 3.9, 9 4.9, 11 5.10, 13

6. Answers 1. 9, 72 < x < 16 2.12, 93 < x < 21 3.9, 90 < x < 18 4.9, 112 < x < 20 5.10, 133 < x < 23