SOLUTION: The figure below shows a rectangle ABCD having diagonals AC and DB. Joshua wrote the following proof to show that the diagonals of rectangle ABCD are congruent. Joshua

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Question 697413: The figure below shows a rectangle ABCD having diagonals AC and DB.


Joshua wrote the following proof to show that the diagonals of rectangle ABCD are congruent.

Joshua’s proof:
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)
Statement 2: AB = DC (by transitive property of equality)
Statement 3: AC2 = DB2 (from statements 1 and 2)
Statement 4: AC = DB (taking square root on both sides of AC2 = DB2)
Which statement in Joshua’s proof has an error?
Answer by jim_thompson5910(35256)   (Show Source): 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.

So I'd say statement 2 is one of the errors.
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