Question

use the diagram to determine whether you can assume the statement.
diagram of planes w and x with points q, r, n, k, j, l, m, p
planes w and x intersect at $overleftrightarrow{kl}$.
$circ$ yes, you can assume the statement.
$circ$ no, you cannot assume the statement.

Explanation:

To determine if planes \( W \) and \( X \) intersect at \( \overleftrightarrow{KL} \), we recall the postulate that the intersection of two planes is a line. From the diagram, we observe the line of intersection of planes \( W \) and \( X \). The line \( \overleftrightarrow{KL} \) is part of the intersection? Wait, no—wait, actually, looking at the diagram, the intersection of planes \( W \) and \( X \) appears to be a different line (maybe the dashed line with points like \( N \), \( K \), etc.? Wait, no, let's re - examine. The key is: when two planes intersect, their intersection is a line. Now, does \( \overleftrightarrow{KL} \) lie on both planes? From the diagram, \( K \) and \( L \) are on the middle plane and plane \( X \)? Wait, no, the diagram shows plane \( W \) (left), a middle plane, and plane \( X \) (right). Wait, maybe I misread. Wait, the problem says planes \( W \) and \( X \). Let's think about the intersection of two planes: the set of all points common to both planes is a line. Now, in the diagram, the line of intersection of \( W \) and \( X \) – does \( \overleftrightarrow{KL} \) lie on both \( W \) and \( X \)? From the diagram, \( K \) and \( L \) – \( K \) is on the middle plane and maybe \( X \), but \( W \) is the left plane. Wait, maybe the correct approach is: the intersection of two planes is a line. If \( \overleftrightarrow{KL} \) is not the line where \( W \) and \( X \) meet (for example, if the actual intersection line is another line, like the one with \( N \), \( K \), etc.), then we can't assume \( W \) and \( X \) intersect at \( \overleftrightarrow{KL} \). Wait, maybe the diagram shows that the intersection of \( W \) and \( X \) is a different line (like the dashed line with \( N \), \( K \), maybe extending), and \( \overleftrightarrow{KL} \) is not that line. So, we cannot assume that planes \( W \) and \( X \) intersect at \( \overleftrightarrow{KL} \).

Answer:

No, you cannot assume the statement.