\n" ); document.write( "Could you please help me with this question?\r
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![\"IMG-4943\"](\"https://i.ibb.co/N9MfcLL/IMG-4943.jpg\")
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document.write( "Algebra.Com's Answer #817249 by robertb(5830)![\"\"](\"/images/stars/stars-13.gif\")  You can put this solution on YOUR website! Although I would agree with the arguments of @greenestamps, any student of Euclidean geometry would serve him/her well \n" ); document.write( "if no assumptions were made based on the diagrams or pictures of the object. @greenestamps' (and also @ josgarithmetic's) arguments \n" ); document.write( "hinges on the fact that X, Z, and Y are collinear, which would make angle XZW a RIGHT triangle. \r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "But this is not completely clear from the drawing, as \n" ); document.write( "1) Nothing in the hypothesis tells us that the figure WXY is a triangle, and so should not be initially treated as such, and consequently \n" ); document.write( "2) It cannot be assumed that angle XZW is a right angle, because it wasn't stated as a hypothesis -- indeed there was no indication of a \"square corner\" at angle XZW. \r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The remedy is to first show that triangle XZW is a right triangle. \n" ); document.write( "The easiest way to prove this is to use the fact that the Pythagorean theorem is an \"if and only\" statement, \n" ); document.write( "i.e., a triangle is a right triangle if and only if the square of one side is the sum of the squares of the other two sides.\r \n" ); document.write( "\n" ); document.write( "From the given figure side WZ will have length \n" ); document.write( "This then will confirm that the sides of triangle XZW satisfy the Pythagorean relation: \n" ); document.write( "and therefore triangle XZW is indeed a right triangle. And consequently, X, Z, and Y are collinear. \n" ); document.write( " |