Question

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.

Answer 1

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)

Answer 2

Which statement in Joshua’s proof has an error?

A) Statement 2
B) Statement 1
C) Statement 3
D) Statement 4

Answer 3

@ghazi @hartnn can any of you help me out?