Question

select the correct answer from each drop - down menu. determine how the figure helps to verify the triangle inequality theorem. the two sides with lengths of 7 and 5 will, which shows that the of the lengths of the two sides of a triangle must be the length of the third side.

Explanation:

Step1: Recall triangle inequality theorem

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

Step2: Analyze given side lengths

Here, two side lengths are 7 and 5. Their sum is \(7 + 5=12\). In the figure, when we try to form a triangle with these two sides and a third - side of length 12, the two arcs (drawn with radii 7 and 5 from the endpoints of the side of length 12) just touch each other. This implies that when the sum of two sides (\(7 + 5\)) is equal to the third side (12), a triangle is not formed.

Answer:

The two sides with lengths of 7 and 5 will not form a triangle, which shows that the sum of the lengths of the two sides of a triangle must be greater than the length of the third side.