Question

The figure below shows a rectangle ABCD having diagonals AC and DB.
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 are congruent)
Statement 3: AC2 = DB2

Answer 1

statement 3:AC2=DB2(from statements 1 and 2)
statement 4:AC=DB (taking square root on both sides of AC^2=DB^2)

Which statement in Anastatia's proof has an error?

a)statement 1
b)statement 3
c)statement 2
d)statement 4

Answer 2

@phi

Answer 3

@phi

Answer 4

@amistre64

Answer 5

@amistre64

Answer 6

statement 1 is so complicated it is hard to say...
the other 3 statements appear correct

Answer 7

so a would be my answer?

Answer 8

@phi

Answer 9

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

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)

Symmetric Property of Equality: if a=b, then b=a
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i dont see how the writeup conforms to the property they describe

Answer 10

so the answer is A? @amistre64

Answer 11

geometric proofs are not my strong point .... but from what i can tell; the property they are trying to apply does not fit what they have written.

Answer 12

my best guess is that A is off, but i cant be sure of it

Answer 13

thank you @amistre64

Answer 14

good luck :)