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Projectors & TVs
If your laptop is connected to a projector, you should be comfortable toggling it between mirroring your laptop's screen and extending your screen so you can be looking at different content.
Windows key + P
Command + F1 (the brightness down button) is the keyboard shortcut. You can also load up your display settings if you prefer the tedious method:
Look for a button on your remote that says Freeze Screen. If you're going to draw on the screen, it's a great way to hold everything still. You can also freeze the screen if you had to bring up a file or modify attendance and you didn't want students distracted by the brief bit of business you had to do.