Question

A rectangle ABCD is shown with diagonals AC and BD.

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)