document.write( "Question 697413: The figure below shows a rectangle ABCD having diagonals AC and DB.
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\n" ); document.write( "Joshua wrote the following proof to show that the diagonals of rectangle ABCD are congruent.
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\n" ); document.write( "Joshua’s proof:
\n" ); document.write( "Statement 1: In right triangle ADC, the sum of the squares of sides AD and DC is equal to the square of hypotenuse AC so that AD2 + DC2 = AC2 and in right triangle ABD, the sum of the square of sides AD and AB is equal to the square of hypotenuse DB so that AD2 + AB2 = DB2 (by Pythagorean Theorem)
\n" ); document.write( "Statement 2: AB = DC (by transitive property of equality)
\n" ); document.write( "Statement 3: AC2 = DB2 (from statements 1 and 2)
\n" ); document.write( "Statement 4: AC = DB (taking square root on both sides of AC2 = DB2)
\n" ); document.write( "Which statement in Joshua’s proof has an error? \n" ); document.write( "

Algebra.Com's Answer #429974 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Statement 2 seems a bit off because you need AB = x and x = DC to use the transitive property of equality, but you don't have such a statement.\r
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\n" ); document.write( "\n" ); document.write( "So I'd say statement 2 is one of the errors. \n" ); document.write( "

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