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

[astrololo]

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!

 

[Mark44]

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 ?

That's how a parallelograph is defined.

 

[astrololo]

That's how a parallelograph is defined.

But couldn't this be a rectangle ?

 

[Mark44]

A rectangle is one type of parallelogram, one in which all four interior angles are equal.

 

[astrololo]

A rectangle is one type of parallelogram, one in which all four interior angles are equal.

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

 

[Mark44]

Ok, then he's not pointing to any specific case, just that we have a general parallelogram ? (That usually have 2 pairs of parallels)

Fixed the above for you: "That usually always 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

 

[astrololo]

Fixed the above for you: "That usually always have 2 pairs of parallels"

thank you !