# Parts of parallel lines are parallel is a postulate or theorem?

• Feb 23rd 2011, 03:32 AM
lamp23
Parts of parallel lines are parallel is a postulate or theorem?
I encountered a proof problem where I was given parallelogram ABCD and that AE is congruent to FC. I had to prove EBFD was a parallelogram. I want to use the theorem that if one pair of sides of a quadrilateral is both congruent and parallel, then it is a parallelogram. In doing so, I would like to say that EB is parallel to FD because parts of parallel lines are parallel. Is that a postulate?http://i900.photobucket.com/albums/a...abcdparall.jpg
• Feb 23rd 2011, 05:45 AM
bjhopper
Hello lamp23,
Yes its a postulate but what makes the other pair parallel

bjh
• Feb 23rd 2011, 09:54 AM
scounged
Quote:

Originally Posted by lamp23
I encountered a proof problem where I was given parallelogram ABCD and that AE is congruent to FC. I had to prove EBFD was a parallelogram. I want to use the theorem that if one pair of sides of a quadrilateral is both congruent and parallel, then it is a parallelogram. In doing so, I would like to say that EB is parallel to FD because parts of parallel lines are parallel. Is that a postulate?http://i900.photobucket.com/albums/a...abcdparall.jpg

If I were you I'd prove the parallelogram by using simple facts about triangles and angles.
• Feb 23rd 2011, 10:26 AM
lamp23
Right, I understand that I can do it with angles but what was first apparent to me was using the theorem that if a quadrilateral has one pair of opposite sides that is both parallel and congruent then it is a parallelogram. Anyway, I wrote this:

S: (line segment)AB || (line segment)DC R: Opposite sides of parallelograms are parallel.

S: (line segment)EB || (line segment)DF R: Line segments contained within parallel lines are parallel.

I wasn't sure if somewhere in the proof I should be including another statement that says (line)AB || (line)DC
• Feb 23rd 2011, 11:11 AM
bjhopper
parallelogram
Hi lamp23,

ABCD is a parallelogram
AE is congruent FC
Prove EBFD is a parallelogram

Angle A = Angle C why
AE = CF given
AD = BC why
Triangles DAE and BCF are congruent why

continue and prove that DE is parallel toFB

bjh
• Feb 23rd 2011, 05:33 PM
lamp23
Quote:

Originally Posted by bjhopper
Hi lamp23,

ABCD is a parallelogram
AE is congruent FC
Prove EBFD is a parallelogram

Angle A = Angle C why
AE = CF given
AD = BC why
Triangles DAE and BCF are congruent why

continue and prove that DE is parallel toFB

bjh

It's not that I'm having trouble find a proof. I just wanted to know if the proof I chose was valid (which it would be as long as "Line segments contained within parallel lines are parallel." is a postulate).
• Feb 24th 2011, 01:26 AM
HallsofIvy
"Parts of parallel lines are parallel" is neither a postulate nor a theorem because we do not define "parallel segments". I think what you want to say is not that "part of the line" or "segments of the line" are parallel but that the two segments lie on parallel lines. Once you have said that you can use the fact that the lines, not the segments, are parallel.