Question

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

Answer 1

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

Answer 2

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 are congruent)
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?

Answer 3

Hello?

Answer 4

Isn't this --> 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)
true by the Pythagorean Theorem?

Answer 5

um...big words

Answer 6

This proof is usually done by applying the SAS Triangle Congruence Postulate.

I'm reading the posted proof which I think may have a typo somewhere in:

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)

And, if you don't know the Pythagorean Theorem or the Symmetric Property of Equality, then you may have trouble recognizing the error in my opinion.