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.

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Presentation transcript:

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: =18 (this is bigger than 7) 12+7=19 (this is bigger than 6) 6+7=13 (this is bigger than 12)

Lets Practice Do the three sides form a triangle? 1.10, 9, , 27, , 10, 7 4.3, 8, , 9, 23

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

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

Practice Give the range for the missing side as one statement. 1.9, , 9 3.9, 9 4.9, , 13

Answers 1. 9, 72 < x < , 93 < x < , 90 < x < , 112 < x < , 133 < x < 23