Question

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

Explanation:

Step1: Recall naming of planes

A plane can be named by any three non - collinear points on the plane. Points \(F\), \(B\), and \(A\) are non - collinear points on plane \(X\), so another name for plane \(X\) can be plane \(FBA\).

Step2: Identify coplanar points

Coplanar points lie on the same plane. Since \(A\), \(B\), \(C\), and \(F\) lie in plane \(X\), we can choose \(B\), \(C\), \(F\) (answers can vary as long as they are points in plane \(X\)).

Step3: Identify collinear points

Collinear points lie on the same line. If we assume there is a line passing through \(B\) and \(C\), then \(B\) and \(C\) are collinear (answers can vary depending on the actual lines in the figure, but since \(B\) and \(C\) seem to be on a possible line, we can choose \(B\)).

Step4: Identify intersecting lines

The line \(\overleftrightarrow{ED}\) intersects the plane \(X\) at point \(B\). If we consider a line like \(\overleftrightarrow{AB}\) (which lies in plane \(X\)), \(\overleftrightarrow{ED}\) and \(\overleftrightarrow{AB}\) are distinct lines that intersect at point \(B\).

Answer:

(a) \(FBA\)
(b) \(B\), \(C\), \(F\)
(c) \(B\)
(d) \(\overleftrightarrow{AB}\)