Question

Suppose Adeline considers what happens when the sum of the lengths of two sides of a triangle is equal to the length of the third side when proving the converse of the triangle inequality theorem. What type of proof will she use?(1 point)

a direct proof

an indirect proof

a two-column proof

a flow chart proof

PLEASE HELP ITS SO URGENT

Answer 1

Adeline will use an indirect proof to show that a triangle cannot exist if the sum of two sides equals the length of the third side, as this leads to a contradiction with the triangle inequality theorem.

Step-by-step explanation:

When Adeline is considering the scenario where the sum of the lengths of two sides of a triangle is equal to the length of the third side in the context of proving the converse of the triangle inequality theorem, she is dealing with a specific case that leads to a degenerate triangle (a triangle with no area). This is because a triangle cannot exist if any two sides' lengths summed together are exactly equal to the length of the third side. In proving this, she would typically rely on an indirect proof, also known as proof by contradiction. An indirect proof would start by assuming the opposite of what needs to be proven and then showing that this assumption leads to a contradiction, thus proving the converse of the triangle inequality theorem.

Answer 2

Indirect Proof

Step-by-step explanation:

I had the same question on my test, upon doing the reading in my lesson, it stated, "To prove the converse, use an indirect proof. So, assume that AB, AC, and BC are the sides of triangle ABC. You must show that |AB|+|AC|≤|BC|, |AB|+|BC|≤|AC| , and |BC|+|AC|≤|AB|". This is discussing the converse of the triangle inequality theorem , which is what the question is asking.