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

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)

3.how is solving radical equations different than solving linear equations?

step-by-step explanation: