Question

The figure below shows a rectangle ABCD having diagonals AC and DB.
A rectangle ABCD is shown with diagonals AC and BD.
Anastasia wrote the following proof to show that the diagonals of rectangle ABCD are congruent.
Anastasia'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 symmetric property of equality
Statement 2: AB = DC opposite sides of a rectangle

Answer 1

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 Anastasia's proof has an error?

Statement 1

Statement 3

Statement 2

Statement 4

Answer 2

The justification for step one seems incorrect, the more appropriate justification would be the Pythagorean theorem.

Answer 3

well the problem is we haven't learned that yet. for some reason we are doing proofs before like actual real geometry. so which one would you chose

Answer 4

I would choose statement 1.

Answer 5

thank you