Question

Indirect proofs help!

Answer 1

The following is an indirect proof of the Addition Property of Equality: For real numbers a, b, and c, if a = b, then a + c = b + c.

Assume____________. According to the given information, a = b. By the Subtraction Property of Equality, one can subtract the same number from both sides of an equation without changing the equation. Therefore, a + c − c ≠ b + c − c. Through subtraction, the c's cancel and a ≠ b. This contradicts the given information so a + c = b + c.

Which statement accurately completes the proof?

a + c = b + c
a + c ≠ b + c
a ≠ b
b = c

Answer 2

@Directrix

Answer 3

In an indirect proof, the technique is to accept the hypothesis and temporarily negate the conclusion. The concept is that the implication is true or false, one or the other. If you assume that it is false and arrive at a contradiction to other theorems already proven true, then the false assumption is itself false, and the original statement of the theorem is true.

Answer 4

Assume that a, b, and c are real numbers with a = b and that a + c ≠ b + c.

Answer 5

Then, pick up the indirect proof from your post:

According to the given information, a = b. By the Subtraction Property of Equality, one can subtract the same number from both sides of an equation without changing the equation. Therefore, a + c − c ≠ b + c − c. Through subtraction, the c's cancel and a ≠ b. This contradicts the given information so a + c = b + c.

Answer 6

Thanks alot :) can you help with 1 more?

Answer 7

This proof is not finished yet.

Answer 8

Ok

Answer 9

What do you think is the last statement of the proof?

Answer 10

It ends when what we assumed was false is shown to be true. So, which option is that?

Answer 11

Answer is A

Answer 12

That is what I think. This question is a little odd.

Answer 13

Or, worded oddly.

Answer 14

Yeah thats why I was confused :P

Answer 15

Can you help with 1 more? @Directrix

Answer 16

I can try.

Answer 17

Ok thank you! Given line AE and line BD that intersect at point C, the following is an indirect paragraph proof proving that vertical angles ACB and ECD are congruent:

lines AE and BD intersect at point C

Assume ∠ACB and ∠ECD are not congruent. The Vertical Angles Theorem says that vertical angles must be congruent. Since this contradicts the assumption, vertical angles ACB and ECD are congruent.

Is the indirect proof logically valid? If so, why? If not, why not?

Yes. Statements are presented in a logical order using the correct theorems.
Yes. The conclusion was used to contradict the assumption.
No. The conclusion was used to contradict the assumption.
No. The progression of the statements is logically inaccurate.

Answer 18

I think its C. but not sure : /

Answer 19

Why did you not choose this:
Yes. The conclusion was used to contradict the assumption.

or maybe

Yes. Statements are presented in a logical order using the correct theorems.

Answer 20

I would have started the proof this way:

lines AE and BD intersect at point C. Assume ∠ACB and ∠ECD are vertical angles and are not congruent.

Answer 21

Hmm, I think it is A

Answer 22

They look to be in the correct order. And I know its not D

Answer 23

I could argue for A or B but in trying to read the mind of whoever wrote the problem, I think the answer is A. If that turns out to be incorrect, then challenge your teacher to show why.

Answer 24

ok thank you directrix you're the best!

Answer 25

You are welcome.

Answer 26

And it was wrong lol

Answer 27

Not A

Answer 28

Do we get another chance?

Answer 29

How does your text define "logically valid?: That may give a clue to the correct answer.

Answer 30

Yes but I probably dont have the same question

Answer 31

Well, what do we have to lose by trying again?

Answer 32

Did the computer program give what 'it" thinks is the correct answer to that question?

Answer 33

This is my last submission on this test and its not on here again, but thanks for trying

Answer 34

No the correct answers are set in stone

Answer 35

ok thanks man Im closing this post

Answer 36

Okay. I'm so sorry about the bad answer.

Answer 37

All good :)