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) $overleftrightarrow{ed}$ and are distinct lines that intersect. (b) and c are distinct points that are collinear. (c) another name for plane x is plane. (d) a, , , and are distinct points that are coplanar.

Explanation:

Step1: Identify intersecting line

The line $\overleftrightarrow{ED}$ intersects the plane $X$ at point $B$. A line in the plane $X$ that intersects $\overleftrightarrow{ED}$ can be $\overleftrightarrow{AB}$.

Step2: Identify collinear points

Points on the same - line are collinear. Points $A$ and $C$ lie on the same vertical line in plane $X$, so $A$ and $C$ are collinear.

Step3: Name the plane

A plane can be named by three non - collinear points in the plane. Points $F$, $C$, and $B$ are non - collinear points in plane $X$, so plane $X$ can be called plane $FCB$.

Step4: Identify coplanar points

Points that lie in the same plane are coplanar. Points $A$, $B$, $C$, and $F$ all lie in plane $X$.

Answer:

(a) $\overleftrightarrow{AB}$
(b) $A$
(c) $FCB$
(d) $B$, $C$, $F$