Which of the following is the statement of the triangle inequality theorem? a. the sum of the measures of any two angles of a triangle is greater than the measure of the third angle. b. the sum of the lengths of any two sides of a triangle is greater than the length of the third side. c. the longest side of a triangle is opposite the largest angle. d. the largest angle of a triangle is between the two longest sides.

The sum of the lengths of any two sides of a triangle is greater than the length of the third side ⇒ answer B

Step-by-step explanation:

* Lets explain the triangle inequality theorem

- The triangle Inequality Theorem is the sum of the lengths of any two

  sides of a triangle is greater than the length of the third side.

- That means when we add the lengths of the shortest two sides,

  the answer will be greater than the length of the longest side.

- Examples:

# Is the set of {4 , 5 , 9} could form a triangle

- Add 4 , and 5 because they are the shortest sides

∵ 4 + 5 = 9

∵ The third side is 9

∵ In any triangle the sum of the lengths of any two sides of a triangle

  must be greater than the length of the third side

∴ The set {4 , 5 , 9} couldn't form a triangle

# Is the set of {4 , 5 , 8} could form a triangle

- Add 4 , and 5 because they are the shortest sides

∵ 4 + 5 = 9

∵ The third side is 8

∵ In any triangle the sum of the lengths of any two sides of a triangle

  must be greater than the length of the third side

∴ The set {4 , 5 , 8} could form a triangle

# Is the set of {3 , 5 , 9} could form a triangle

- Add 3 , and 5 because they are the shortest sides

∵ 3 + 5 = 8

∵ The third side is 9

∵ In any triangle the sum of the lengths of any two sides of a triangle

  must be greater than the length of the third side

∴ The set {3 , 5 , 9} couldn't form a triangle

* Lets solve the problem

∵ The triangle inequality theorem is the sum of the lengths of any two

  sides of a triangle is greater than the length of the third side

- It talks about the relation between the lengths of the sides

∴ The right answer is B. The sum of the lengths of any two sides of

   a triangle is greater than the length of the third side

answer: true

step-by-step explanation:

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step-by-step explanation: