Question

Help me Please:
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:

Answer 1

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 2

Statement 1

Statement 3

Statement 2

Statement 4

Answer 3

Figure: http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_1000_Subtest_04_15/image0034e8c6dfa.jpg

Answer 4

@KingGeorge

Answer 5

The only "error" I can find, is one of the facts used isn't the right fact to use. In other words, the statement is correct, but the reasoning (the stuff in parentheses) is wrong.

By looking at the problem in this way, where do you think the error is?

Answer 6

i think it might be the fourth one i have no idea im really bad with proofs

Answer 7

The fourth step looks a little suspicious because of the square root, but since we're always dealing with positive length, the 4th step is fine.

The actual error is in the first step. What should the reasoning for the first step actually be?

Answer 8

What fact/theorem should we use instead of "symmetric property of equality?"

Answer 9

corrisponding angles i think

Answer 10

Nope. Suppose I have a right triangle with legs of length a,b and hypotenuse of length c. What famous theorem tell me that \(a^2+b^2=c^2\)?

Answer 11

pythagorean theorem

Answer 12

Right. That should be the reasoning for the first step.

Answer 13

ok thanks soo mutch

Answer 14

You're welcome.