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

Answer 2

we know that

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

Let

a,b,c------> the length sides of a triangle

The theorem states that three conditions must be met

case 1)

`a+b > c`

case 2)

`a+c > b`

case3)

`c+b > a`

therefore

the answer is the option

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