Answer:
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
