Which set of line segments can be used to construct a triangle?

Responses
A 8 cm, 3 cm, and 6 cm8 cm, 3 cm, and 6 cm
B 7 cm, 4 cm, and 1 cm7 cm, 4 cm, and 1 cm
C 6 cm, 3 cm, and 2 cm6 cm, 3 cm, and 2 cm
D 9 cm, 2 cm, and 6 cm

1 answer

The set of line segments that can be used to construct a triangle is the one that satisfies 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 B since 7 cm + 4 cm is not greater than 1 cm.

Option D can also be eliminated since 9 cm + 2 cm is not greater than 6 cm.

Option A satisfies the theorem since 8 cm + 3 cm is greater than 6 cm, and 8 cm + 6 cm is greater than 3 cm.

Option C also satisfies the theorem since 6 cm + 3 cm is greater than 2 cm, and 6 cm + 2 cm is greater than 3 cm.

Therefore, the sets of line segments that can be used to construct a triangle are options A and C.