Nila is constructing triangles for her math project. Choose ALL sets of line segment lengths that Nila can use.

Question

Nila is constructing triangles for her math project. Choose ALL sets of line segment lengths that Nila can use.

Responses
A 1 in, 2 in, 2 in1 in, 2 in, 2 in
B 2 in, 2 in, 6 in2 in, 2 in, 6 in
C 5 in, 5 in, 5 in5 in, 5 in, 5 in
D 4 in, 6 in, 6 in4 in, 6 in, 6 in
E 3 in, 4 in, 7 in

Answer 1

A, B, and D are sets of line segment lengths that Nila can use to construct triangles. C is a set of lengths for an equilateral triangle, which is a type of triangle but may not fit the requirements of Nila's project. E violates the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side. Therefore, option E cannot be used to construct a triangle.