Question

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

Explanation:

Step1: Analyze intersecting lines

We need to find a line that intersects $\overleftrightarrow{DC}$. Since points $D,B,E,F,G$ are in plane $X$ and $A$ and $C$ are outside, a possible line could be $\overleftrightarrow{DB}$ as it has a common - point $D$ with $\overleftrightarrow{DC}$ and is a distinct line.

Step2: Name the plane

A plane can be named by any three non - collinear points in the plane. Points $D$, $B$, and $E$ are non - collinear points in plane $X$, so another name for plane $X$ is plane $DBE$.

Step3: Find collinear points

Points that lie on the same line are collinear. Since $E$, $F$, and $G$ lie on the same line in the figure, $E$ (or $G$) and $F$ are distinct points that are collinear.

Step4: Find coplanar line

Since point $D$ is in plane $X$, any line in plane $X$ is coplanar with point $D$. For example, $\overleftrightarrow{EF}$ is in plane $X$ and is coplanar with point $D$.

Answer:

(a) $\overleftrightarrow{DB}$
(b) $DBE$
(c) $E$ (or $G$)
(d) $\overleftrightarrow{EF}$