Question

in the figure below, points n, k, j, and h lie in plane z. points l and m do not lie in plane z. for each part below, fill in the blanks to write a true statement. (a) another name for plane z is plane . (b) point n and line are coplanar. (c) k, , and are distinct points that are collinear. (d) $overleftrightarrow{lm}$ 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 $N$, $K$, and $J$ are non - collinear points on plane $Z$, so another name for plane $Z$ is plane $NKJ$.

Step2: Identify coplanar line with point $N$

Since points $N$, $K$, $J$, $H$ lie in plane $Z$, a line formed by any two of these points will be coplanar with point $N$. For example, line $\overleftrightarrow{KJ}$ lies in plane $Z$ and is coplanar with point $N$.

Step3: Find collinear points

Points $H$, $J$, $K$ appear to lie on the same vertical line in the plane $Z$, so $K$, $J$, and $H$ are distinct collinear points.

Step4: Find intersecting line with $\overleftrightarrow{LM}$

The line $\overleftrightarrow{LM}$ intersects the plane $Z$. If we consider the line formed by extending the intersection of the vertical line in the plane $Z$ with the line $\overleftrightarrow{LM}$, we can see that $\overleftrightarrow{LM}$ and $\overleftrightarrow{KJ}$ intersect (assuming the lines are extended as needed).

Answer:

(a) $NKJ$
(b) $\overleftrightarrow{KJ}$
(c) $J$, $H$
(d) $\overleftrightarrow{KJ}$