Final answer:
No triangles can be formed using segments of lengths 4 cm, 4.5 cm, and 9 cm, as they violate the Triangle Inequality Theorem, which requires the sum of any two sides to be greater than the third.
Step-by-step explanation:
To determine how many triangles can be formed using segments of given lengths, we must remember the Triangle Inequality Theorem. This 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. Given the segments of lengths 4 cm, 4.5 cm, and 9 cm, we add the shorter two segments (4 + 4.5 = 8.5 cm) and compare this sum to the length of the longest segment (9 cm).Since 8.5 cm is not greater than 9 cm, these segments do not satisfy the Triangle Inequality Theorem. Therefore, it is not possible to form a triangle with these segment lengths. The number of triangles that can be formed is zero.
Write the final answer in 20 words: No triangles can be formed with 4 cm, 4.5 cm, and 9 cm segments, due to the Triangle Inequality Theorem.To determine how many triangles can be formed using segments of lengths 4 cm, 4.5 cm, and 9 cm, we need to apply the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.In this case, let's compare the lengths. The sum of 4 cm and 4.5 cm is 8.5 cm, which is less than 9 cm. Therefore, it is not possible to form a triangle with these lengths.So the answer is a) 0 triangles.