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) and k are distinct points that are collinear. (b) $overleftrightarrow{ml}$ and are distinct lines that intersect. (c) h, , , and are distinct points that are coplanar. (d) another name for plane z is plane .

Explanation:

Step1: Recall collinear points

Collinear points lie on the same line. From the figure, points $J$ and $K$ lie on the same vertical - like line in plane $Z$. So, $J$ and $K$ are collinear.

Step2: Recall intersecting lines

Intersecting lines meet at a point. Line $\overleftrightarrow{ML}$ intersects the vertical - like line in plane $Z$ at point $J$. So, $\overleftrightarrow{ML}$ and $\overleftrightarrow{JK}$ (or $\overleftrightarrow{HJ}$) intersect. Let's choose $\overleftrightarrow{JK}$.

Step3: Recall coplanar points

Coplanar points lie in the same plane. Points $H$, $J$, $K$, and $N$ all lie in plane $Z$.

Step4: Name a plane

A plane can be named by three non - collinear points in the plane. Points $H$, $J$, $N$ are non - collinear points in plane $Z$. So, another name for plane $Z$ is plane $HJN$.

Answer:

(a) $J$
(b) $\overleftrightarrow{JK}$
(c) $J$, $K$, $N$
(d) $HJN$