Question

which statements are true? select all that apply. one line can be drawn connecting points l, m, and n. exactly one line can be drawn through point n that is parallel to a line drawn through points l and m. if m is the center of a circle, then points l and n lie on the circle. points l, m, and n determine a plane.

Explanation:

Step1: Recall geometric post - ulates

One of the fundamental postulates in geometry states that exactly one line can be drawn through two distinct points. So, exactly one line can be drawn through points L and M.

Step2: Analyze the concept of lines through three non - collinear points

Three non - collinear points (L, M, N) determine a plane, but only one line can be drawn through two of them (e.g., L and M). And it is not always possible to draw a line through N parallel to a line through L and M in all cases. Also, it is not true that one line can be drawn connecting L, M, and N as three non - collinear points do not lie on a single line. If M is the center of a circle and L and N are on the circle, they are not necessarily collinear with the center in a way that would support the given statements.

Answer:

Exactly one line can be drawn through points L and M.