Question

in the figure below, points a, e, f, and c lie in plane x. points b and d do not lie in plane x. for each part below, fill in the blanks to write a true statement. (a) d, \\(\square\\), and \\(\square\\) are distinct points that are collinear. (b) \\(\overleftrightarrow{ef}\\) and \\(\square\overleftrightarrow{\square}\\) are distinct lines that intersect. (c) point a and line \\(\square\overleftrightarrow{\square}\\) are coplanar. (d) another name for plane x is plane \\(\square\\).

Explanation:

Step1: Analyze part (a)

Collinear points lie on the same line. Points \(D\), \(C\), and \(B\) are on the same line.

Step2: Analyze part (b)

Lines that intersect: \(\overleftrightarrow{EF}\) and \(\overleftrightarrow{BC}\) intersect at point \(C\)

Step3: Analyze part (c)

Coplanar means in the same plane. Point \(A\) and line \(\overleftrightarrow{EF}\) are in plane \(X\)

Step4: Analyze part (d)

A plane can be named by three non - collinear points. Plane \(X\) can also be named plane \(ACF\) (or other combinations of non - collinear points in the plane like \(AEF\), \(AEC\) etc.)

Answer:

(a) \(C\), \(B\) (b) \(\overleftrightarrow{BC}\) (c) \(\overleftrightarrow{EF}\) (d) \(ACF\) (answers for (d) can vary as long as it is a valid name for the plane using non - collinear points in plane \(X\))