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

Explanation:

Step1: Recall coplanar concept

Coplanar means lying on the same plane. Since points $A$, $E$, $F$, $C$ lie in plane $X$, any line formed by these points will be coplanar with point $A$. For example, line $\overleftrightarrow{EF}$.

Step2: Name a plane by three non - collinear points

A plane can be named by any three non - collinear points on the plane. Points $A$, $E$, $C$ are non - collinear points on plane $X$, so plane $X$ can be called plane $AEC$.

Step3: Find intersecting lines

Lines that intersect must meet at a point. $\overleftrightarrow{EF}$ and $\overleftrightarrow{AC}$ intersect at a point (assuming they are not parallel in the context of the plane), and they are distinct lines.

Step4: Recall collinear concept

Collinear points lie on the same line. Points $B$, $C$, $D$ seem to lie on the same vertical line (from the figure), so $D$, $B$, $C$ are collinear.

Answer:

(a) $\overleftrightarrow{EF}$
(b) $AEC$
(c) $\overleftrightarrow{AC}$
(d) $B$, $C$