Question

14 use the diagram to determine if each statement is true or false. a) points a, b, d, and j are coplanar. b) points e, g, and a are collinear. c) $overline{fg} perp$ plane $mathcal{z}$ d) $overrightarrow{fg}$ and $overrightarrow{de}$ intersect. e) planes $mathcal{z}$ and $mathcal{k}$ intersect at $overline{ab}$. f) $overline{ge}$ is in plane $mathcal{z}$

Explanation:

To solve this, we analyze each statement using the diagram:

Part (a)

Coplanar points lie on the same plane. Points \( A \), \( B \), \( D \), and \( J \): \( A, B, D \) are on Plane \( \mathcal{Z} \), and \( J \) is also on Plane \( \mathcal{Z} \) (from the diagram). So they are coplanar.

Answer:

** True

Part (b)

Collinear points lie on the same line. Points \( E \), \( G \), and \( A \): \( E, G \) are on Plane \( \mathcal{X} \), but \( A \) is on Plane \( \mathcal{Z} \). No line contains all three, so they are not collinear.