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Triangles which are on the same base and in the same paralle

  1. May 20, 2015 #1
    I have a small question regarding proposition 37 of the elements of Euclid. http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI37.html

    The only problem I got with the proof is the fact that we don't seem to prove that we do have parallelogram. We have a figure with 4 side and we know that each opposite sides are parallels to each other. Is this considered enough to acknowledge that we have parallelograms ?

    Thank you!
     
  2. jcsd
  3. May 20, 2015 #2

    Mark44

    Staff: Mentor

    That's how a parallelograph is defined.
     
  4. May 21, 2015 #3
    But couldn't this be a rectangle ???
     
  5. May 21, 2015 #4

    Mark44

    Staff: Mentor

    A rectangle is one type of parallelogram, one in which all four interior angles are equal.
     
  6. May 21, 2015 #5
    Ok, then he's not pointing to any specific case, just that we have a general parallelogram ? (That usually have 2 pairs of parallels) Is that how I'm supposed to understand it ? I did the mistake of assuming that we had a
    Rhomboid
     
  7. May 21, 2015 #6

    Mark44

    Staff: Mentor

    Fixed the above for you: "That usually always have 2 pairs of parallels"
     
  8. May 21, 2015 #7
    thank you !
     
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