Can I use a Blu-Ray DVD player on a non-HD TV?

My traditional DVD player is starting to wear out, so I figure it makes sense to buy a Blu-Ray DVD player; however, the current TV that I have works just fine, but it is not HD or plasma or LCD. Can I hook up a Blu-Ray player to a non-HD TV?

Also, will my traditional, non-Blu Ray DVDs work on a Blu-Ray player, or do I have to upgrade all my movies to Blu-Ray DVDs?

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