Geometry Proofs Help

  1. Geometry Proofs.. Help!!

    Please please someone help me!! :eek: I have a Geometry Exam on :surprised Monday and I don't understand proofs one bit :cry: !! If someone could help me with a few proofs that would be so awesome!!
     
  2. jcsd
  3. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    Have you got any specific questions?
     
  4. yeah, could you help me with this proof..

    Given: B is between A and C; D is between C and E; and C is the midpoint of line BD and of line AE

    Prove: line AB is congruent to line DE

    Picture:

    <--A---B---C---D---E-->
     
  5. yeah, could you help me with this proof..

    Given: B is between A and C; D is between C and E; and C is the midpoint of line BD and of line AE

    Prove: line AB is congruent to line DE

    Picture:

    <--A---B---C---D---E-->
     
  6. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    Ok, I'll give a hint. You know that [tex]|\vec{AC}|=|\vec{CE}|[/tex] so start with this, then express both sides of the equation in terms of two new lengths. Have a go, and post your thoughts.
     
  7. AB+BC= line AC

    and

    CD+CE = line CE

    I don't know, am I even on the right track??
     
  8. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    Yes, so now the equation becomes:[tex]|\vec{AC}|=|\vec{CE}| \Rightarrow
    |\vec{AB}|+|\vec{BC}|=|\vec{CD}|+|\vec{DE}|
    [/tex] Carry on with this.
     
  9. umm.. would the reason be substitution??
     
  10. Line AC is congruent to line CE??
     
  11. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    Ok, my notation
    means that the length of the line AC is equal to the length of the line CE (this is equivalent to the two lines being congruent).

    We know that AC is congruent to CE, since C is the midpoint of AE. CAn you say anything similar regarding the lines BC and CD
     
  12. C is the midpoint of lines BC and CD?
     
  13. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    WEll, C is the midpoint of BD, therefore BC and CD are congruent. Now look at the equation given in post #7. What does this tell you?
     
  14. I don't think I understand.. Can you give me a hint??
     
  15. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    Not without giving you the answer!! Ok, here goes: The equation can be rearranged to give

    [tex]|\vec{AB}|-|\vec{DE}| =|\vec{CD}|-|\vec{BC}|[/tex]
    Now, since the BC and CD are congruent, what can say about the RHS of the equation? What does this then imply?
     
  16. I don't know.. Umm whats a RHS??
     
  17. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    Right hand side. Ok, if two lines are congruent, then it means they have the same length. Lets call this length x. Then the RHS is x-x=...?
     
  18. the lengths are congruent?
     
  19. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    Well, [tex]|\vec{AB}|-|\vec{DE}| =|\vec{CD}|-|\vec{BC}|=0 \Rightarrow |\vec{AB}|=|\vec{DE}|[/tex]

    And so, the lines AB and DE are congruent.
     
  20. Ok, i think i get it.. Thanks.. Do you think you could help me with a couple more??
     
  21. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    Maybe one, it's getting quite late. Post your attempt at a proof to the problem you post first though.
     
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