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) another name for plane x is plane . (b) and f are distinct points that are collinear. (c) point d and line are coplanar. (d) suppose line $overleftrightarrow{dc}$ is drawn on the figure. then $overleftrightarrow{dc}$ and are distinct lines that intersect.

Explanation:

Step1: Recall plane - naming convention

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

Step2: Recall collinear points definition

Points on the same line are collinear. Points $E$ and $F$ lie on the same line, so $E$ and $F$ are distinct collinear points.

Step3: Recall coplanar definition

Coplanar means lying on the same plane. Line $EF$ lies in plane $X$ and point $D$ lies in plane $X$, so point $D$ and line $EF$ are coplanar.

Step4: Find intersecting line

If line $\overleftrightarrow{DC}$ is drawn, line $\overleftrightarrow{DB}$ intersects $\overleftrightarrow{DC}$ at point $D$.

Answer:

(a) $DBE$
(b) $E$
(c) $EF$
(d) $DB$