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) another name for plane z is plane ☐.
(b) m, ☐, ☐, and ☐ are distinct points that are coplanar.
(c) j, ☐, and ☐ are distinct points that are collinear.
(d) $overleftrightarrow{nk}$ and ☐ are distinct lines that intersect.

Explanation:

Part (a)

Step1: Recall plane naming

A plane can be named by three non - collinear points in it. Points H, M, N (or other combinations like H, M, K etc.) lie in plane Z. So another name for plane Z can be plane HMN (or plane HMK, plane MNK, plane HNK etc. as long as the three points are in plane Z).

Step1: Identify coplanar points

Coplanar points lie in the same plane. Points M, N, K, H (or M, N, K, any of the other points in plane Z) are in plane Z. So we can fill in N, K, H (or other valid points from H, N, K as they are in plane Z).

Step1: Identify collinear points

Collinear points lie on the same line. Points J, K, L are on the same vertical line (since J and L are not in plane Z and K is in plane Z, and the line through J, K, L is perpendicular to plane Z at K). So we fill in K and L.

Answer:

HMN (or other valid combination like HMK, MNK, HNK etc.)

Part (b)