Question

in the figure below, points h, m, n, and k lie in plane z.
points j and l do not lie in plane z.
for each part below, fill in the blanks to write a true statement.
(a) \\( \overleftrightarrow { n k } \\) and \\( \overleftrightarrow { j l } \\) are distinct lines that intersect.
(b) j, \\( \square \\), and \\( \square \\) are distinct points that are collinear.
(c) another name for plane z is plane \\( \square \\).
(d) m, \\( \square \\), \\( \square \\), and \\( \square \\) are distinct points that are coplanar.

Explanation:

Part (a)

Step1: Analyze the figure

Looking at the intersection of lines. Line \(\overleftrightarrow{NK}\) and line \(\overleftrightarrow{JL}\) intersect at point \(K\) as shown in the figure.

Part (b)

Step1: Recall collinear points definition

Collinear points lie on the same straight - line. Points \(J\), \(K\), and \(L\) lie on the same vertical line.

Part (c)

Step1: Name a plane by non - collinear points

A plane can be named by three non - collinear points in the plane. Points \(H\), \(M\), \(N\), \(K\) are in plane \(Z\). Using three non - collinear points \(H\), \(M\), \(N\) (or other combinations of three non - collinear points from \(H\), \(M\), \(N\), \(K\)) to name the plane. For example, plane \(HMN\)

Part (d)

Step1: Recall coplanar points definition

Coplanar points lie on the same plane. Points \(M\), \(N\), \(K\), \(H\) all lie in plane \(Z\)

Answer:

(a) \(\overleftrightarrow{JL}\)
(b) \(K\), \(L\)
(c) \(HMN\) (or \(HMK\), \(HNK\), \(MNK\) etc. using three non - collinear points from \(H\), \(M\), \(N\), \(K\))
(d) \(N\), \(K\), \(H\)