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) b, \boxed{}, and \boxed{} are distinct points that are collinear.
(b) overleftrightarrow{fc} and overleftrightarrow{\boxed{}} are distinct lines that intersect.
(c) e, \boxed{}, \boxed{}, and \boxed{} are distinct points that are coplanar.
(d) another name for plane x is plane \boxed{}.

Explanation:

Step1: Analyze part (a)

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

Step2: Analyze part (b)

Lines that intersect: \(\overleftrightarrow{FC}\) and \(\overleftrightarrow{BC}\) (or \(\overleftrightarrow{DC}\) or \(\overleftrightarrow{BD}\)) intersect at point \(C\).

Step3: Analyze part (c)

Coplanar points (points on the same plane \(X\)): \(E\), \(F\), \(A\) (any three non - collinear points on plane \(X\) can be chosen. Since \(A\), \(E\), \(F\) are on plane \(X\) and non - collinear in the context of the figure).

Step4: Analyze part (d)

Another name for a plane can be given by three non - collinear points on the plane. Points \(A\), \(E\), \(F\) (or other combinations of non - collinear points on plane \(X\)) can name the plane. For simplicity, using three non - collinear points \(AEF\) (the order of naming three non - collinear points for a plane is not strict as long as they are on the plane).

Answer:

a. \(C\), \(D\)
b. \(\overleftrightarrow{BC}\) (or \(\overleftrightarrow{DC}\) or \(\overleftrightarrow{BD}\))
c. \(F\), \(A\)
d. \(AEF\)