Don't believe us? We can prove it (with a proof, no less).Ĭlaim: If A = B and B = C and C = D, then A = D. In fact, you can build even longer trains like A = B = C = D, and conclude that A = D. Okay, so that doesn't happen in real life, but it's a good way to remember the transitive property. To remember it, just build a little train that looks like A = B = C and conclude that the engine equals the caboose. This ranks up there with reflexivity in how often it's used in geometry. The transitive property states that if A = B and B = C, then A = C. (Did you notice that it's a conditional statement, too?) This is mainly useful for reorganizing our expressions on the page, since it lets us flip statements across the equal sign. The symmetric property states that if A = B, then B = A. And it's way easier than folding yourself into a ball. The reflexive property may seem obvious (and it is) but it's still useful, especially when dealing with geometrical figures. It doesn't matter how flexible he is he'll still be a contortionist. He'll be a contortionist if he's standing up or if he's sitting on his own head. Think of the reflexive property as the re flexible property. The reflexive property states that A = A. These play a special role in geometry, so they're extra-important to remember. We mean the properties of reflexivity, symmetry, and transitivity. So how do we really know when two things are equal? We rely primarily on properties, and we aren't talking real estate.
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