7.37. What is the maximum number of planes of symmetry that a spatial figure consisting of three pairwise non-parallel lines can have?

Symmetry with respect to a line $l$ is a transformation of space that maps a point $X$ to a point $X^{\prime}$ such that the line $l$ passes through the midpoint of the segment $X X^{\prime}$ and is perpendicular to it. This transformation is also called axial symmetry, and $l$ is called the axis of symmetry:
7.37. Let $P$ be a plane of symmetry of a figure consisting of three pairwise non-parallel lines. There are only two possible cases: 1) each given line is symmetric relative to $P$; 2) one line is symmetric relative to $P$, and the other two lines are symmetric to each other.

In the first case, either one line is perpendicular to $P$, and the other two belong to $P$, or all three lines belong to $P$. Thus, the plane $P$ is defined by some pair of the given lines. Therefore, the number of planes of symmetry of this type is no more than 3.

In the second case, the plane $P$ passes through the bisector of the angle between two given lines and is perpendicular to the plane containing these lines. For each pair of lines, there are exactly 2 such planes, so the number of planes of symmetry of this type is no more than 6.

Thus, the total number of planes of symmetry is no more than 9. Moreover, a figure consisting of three pairwise perpendicular lines passing through one point has exactly 9 planes of symmetry.