The set of line segments that can be used to construct a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Using this theorem, we can eliminate option D since 3 cm + 3 cm = 6 cm, which is not greater than 2 cm.
Option A also cannot be used to construct a triangle since 1 cm + 2 cm = 3 cm, which is not greater than 6 cm.
Option C also fails the triangle inequality theorem since 2 cm + 4 cm = 6 cm, which is not greater than 8 cm.
Therefore, the correct answer is option B, which satisfies the triangle inequality theorem since 3 cm + 4 cm = 7 cm, 4 cm + 9 cm = 13 cm, and 3 cm + 9 cm = 12 cm, and all of these sums are greater than the remaining side length.
Which set of line segments can be used to construct a triangle?
Responses
A 2 cm, 6 cm, and 1 cm2 cm, 6 cm, and 1 cm
B 4 cm, 3 cm, and 9 cm4 cm, 3 cm, and 9 cm
C 4 cm, 2 cm, and 8 cm4 cm, 2 cm, and 8 cm
D 3 cm, 3 cm, and 2 cm
1 answer
1 answer