Question

Peter completed his Geometry test with the following proof. The “Statements” were all provided. He completed the “Reasons”. What error, if any did he make?

Given that M is the midpoint of XY⎯⎯⎯⎯⎯and XY=12, in the following diagram, complete the proof to prove MY=6.
Statement Reason
I am willing to do the work. I will include graph and answers once the question is open.

Answer 1

Statement Reason
1. M is the midpoint of XY⎯⎯⎯⎯⎯ 1. Given
2.XM=MY 2. Definition of a Midpoint of a Segment
3.XM+MY=XY 3. Segment Addition Postulate
4. MY+MY=XY 4. Substitution Property of Equality (steps 2, 3)
5. 2(MY)=XY 5. Addition of Like Terms
6. XY=12 6. Given
7. 2(MY)=12 7. Commutative Proper of Equality
8. MY=6 8. Division Property of Equality

Answer 2

Possible answers:
Step 3


Step 5


Step 7


Peter's proof is correct

Answer 3

@Directrix

Answer 4

Well, we can just go down the list step by step...

Answer 5

Something is not right here:

7. 2(MY)=12 7. Commutative Proper of Equality

Do you see the error?

Answer 6

Give me a second.

Answer 7

Well for starters I don't believe they spelled 'property' right, and secondly it looks to me that the property in use does not maintain equality. Am I correct @Directrix ?

Answer 8

Look at the lines above that statement and follow the flow of the proof.

Is line 7 a logical consequence of what has been said before it.

Answer 9

No. In fact it doesn't make any sense... @Directrix

Answer 10

That may be true but be more specific.

What should be the reason for that step?

Answer 11

Well it's says in the beginning that XY = 12, but the preceding statement before that throws me off slightly...

Answer 12

5. 2(MY)=XY 5. Addition of Like Terms

6. XY=12 6. Given

7. 2(MY)=12 7. Commutative Property of Equality
-------------------

Line 5 2(MY)=XY

6. XY=12

Think about it this way: two things equal to the same thing are equal to each other.

Two "things" are equal to XY.

So they are equal to each other for line 7

7. 2(MY)=12 Substitution (You could argue transitive property as well)

Answer 13

Ahhh. Ok. Ok. That makes sense. I see what your saying now.

Answer 14

The error is that he put commutative property as justification for two quantities equaling each other.

The commutative property has to do with the order of two quantities in addition or multiplication. None of that was going on here.

Answer 15

As always thank you. Thank you for providing detailed explanations!

Answer 16

You are welcome.