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) point n and line are coplanar. (b) another name for plane z is plane. (c) lm and are distinct lines that intersect. (d) k, , and are distinct points that are collinear.

Explanation:

(a)

Step1: Identify coplanar elements

Coplanar means lying on the same plane. Point \(N\) is in plane \(Z\), and line \(KH\) (or \(KJ\), \(JH\) etc. as they are in plane \(Z\)) is in plane \(Z\).

(b)

Step1: Rename the plane

A plane can be named by three non - collinear points in it. Since points \(N\), \(K\), \(J\), \(H\) are in plane \(Z\), another name for plane \(Z\) could be plane \(NKJ\) (or plane \(NJH\), plane \(KJH\) etc.)

(c)

Step1: Find intersecting line

Line \(\overleftrightarrow{LM}\) is not in plane \(Z\). A line that intersects \(\overleftrightarrow{LM}\) and is in the figure: \(\overleftrightarrow{KJ}\) (they intersect at point \(J\))

(d)

Step1: Find collinear points

Collinear points lie on the same straight line. Points \(K\), \(J\), \(H\) are collinear (they lie on the same line in plane \(Z\))

Answer:

(a) Point \(N\) and line \(\overleftrightarrow{KH}\) (or other valid lines in plane \(Z\)) are coplanar.
(b) Another name for plane \(Z\) is plane \(NKJ\) (or other valid combinations of three non - collinear points in plane \(Z\)).
(c) \(\overleftrightarrow{LM}\) and \(\overleftrightarrow{KJ}\) (or other valid intersecting lines) are distinct lines that intersect.
(d) \(K\), \(J\), and \(H\) (or other valid collinear points) are distinct points that are collinear.