Highlighting parent in the top-most navigation

I'm using an always-visible side navigation bar for a web app I'm helping design. This bar serves as the topmost navigation throughout the app, providing fast access to top-most categories even from deeply-nested pages.

It follows this pattern: Navigation drawer mini variant

What I'm wondering is: If I'm on a child page, should the navigation bar highlight the top-most parent? Or should it not highlight anything, since I'm not on the parent page itself?

To clarify, imagine this as the hierarchy:

  • Page 1
    • Subpage 1
    • Subpage 2
  • Page 2
  • Page 3

Only page 1, 2, and 3 are in the side navigation. I'm on subpage 1. Should "Page 1" be highlighted in the side navigation or not?