document.write( "Question 1118469: Let P be the set of all triangles in a plane and R be the relation defined on P as aRb if a is similar
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Algebra.Com's Answer #733796 by ikleyn(52835) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "To prove the equivalence relation, three statements must be proved:\r
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document.write( "1)  each triangle is similar to itself.\r\n" );
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document.write( "    (The proof is obvious).\r\n" );
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document.write( "2)  if triangle \"a\" is similar to triangle \"b\", then the triangle \"b\" is similar to triangle \"a\"  \r\n" );
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document.write( "    (the reflexive property of equivalence, or symmetry property).\r\n" );
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document.write( "    The proof is OBVIOUS, again. All you need to know is the definition of the triangles similarity.\r\n" );
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document.write( "3)  If triangle \"a\" is similar to triangle \"b\"  and  triangle \"b\" is similar to triangle \"c\",  \r\n" );
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document.write( "    then triangle \"a\" is similar to triangle \"c\" (transitivity property of equivalence).\r\n" );
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document.write( "    The proof is OBVIOUS, again. Use the definition of the triangles similarity.\r\n" );
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