Question

Do the given conditions determine one unique triangle, many similar triangles, many nonidentical triangles or no triangle?

5mm, 8mm, 8mm

Answer 1

The given side lengths of 5mm, 8mm, and 8mm satisfy the Triangle Inequality Theorem, meaning they will form one unique isosceles triangle, where two sides are equal.

Step-by-step explanation:

The conditions provided, which are three side lengths of 5mm, 8mm, and 8mm, describe the sides of a triangle and whether these conditions can create a unique triangle, multiple triangles, or no triangle at all. In this case, we can apply the Triangle Inequality Theorem to determine the answer. 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.

For the given lengths 5mm, 8mm, and 8mm, we can create a single, unique triangle. This is because the two sides of 8mm each are both longer than the third side, and the sum of any two sides is always greater than the third side:

• 8mm + 8mm > 5mm
• 8mm + 5mm > 8mm
• 8mm + 5mm > 8mm

Since the conditions meet the Triangle Inequality Theorem, we can conclude that these measurements will form one unique isosceles triangle, wherein two sides are equal in length.