Question

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 1

B

Explanation:

A cannot be correct as it is measuring angles, and the theorem is not abt the angles.

B is correct because the theorem is abt triangle sides.

C is incorrect because that is just ridiculous.

D is incorrect because is not always true and the theorem once again, is not abt angles.

Answer 2

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

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