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.

Answer:The sum of the lengths of any two sides of a triangle is greater than the length of the third side ⇒ answer BStep-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