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

1. ## 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?

2. Hello lamp23,
Yes its a postulate but what makes the other pair parallel

bjh

3. 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?
If I were you I'd prove the parallelogram by using simple facts about triangles and angles.

4. 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

5. ## parallelogram

Hi lamp23,

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

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

continue and prove that DE is parallel toFB

bjh

6. 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