Yoongilife
  • Yoongilife
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.
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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Yoongilife
  • Yoongilife
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
1 Attachment
Yoongilife
  • Yoongilife
Possible answers: Step 3 Step 5 Step 7 Peter's proof is correct
Yoongilife
  • Yoongilife
@Directrix

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rational
  • rational
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Yoongilife
  • Yoongilife
Well, we can just go down the list step by step...
Directrix
  • Directrix
Something is not right here: 7. 2(MY)=12 7. Commutative Proper of Equality Do you see the error?
Yoongilife
  • Yoongilife
Give me a second.
Yoongilife
  • Yoongilife
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 ?
Directrix
  • Directrix
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.
Yoongilife
  • Yoongilife
No. In fact it doesn't make any sense... @Directrix
Directrix
  • Directrix
That may be true but be more specific. What should be the reason for that step?
Yoongilife
  • Yoongilife
Well it's says in the beginning that XY = 12, but the preceding statement before that throws me off slightly...
Directrix
  • Directrix
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)
Yoongilife
  • Yoongilife
Ahhh. Ok. Ok. That makes sense. I see what your saying now.
Directrix
  • Directrix
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.
Yoongilife
  • Yoongilife
As always thank you. Thank you for providing detailed explanations!
Directrix
  • Directrix
You are welcome.

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