Why Prove Things? A Geometry Debate

Earlier this week, my geometry students took part in a new debate format. As is often the case, the topic was student generated. Every year, students inevitably complain about proofs in geometry. It generally happens based on what they have heard from parents  or older friends who have horror stories about their experiences with impossible wastes if time, and it comes up before we do proofs. Once we start doing proofs, students question why we are proving things that were already proven. “Shouldn’t geometry be about measuring angles and lengths and areas and volumes?”, they ask. “Why can’t we just apply what others have proven before us? What’s the point?”

Of course, I have my reasons, but  

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