SOLUTION: Given: Line P is parallel to line Q Line Q is parallel to line R Prove: Line P is parallel to line R

Algebra.Com
Question 1001536: Given: Line P is parallel to line Q
Line Q is parallel to line R
Prove: Line P is parallel to line R

Answer by ikleyn(52857)   (Show Source): You can put this solution on YOUR website!
.

When you have two straight lines in the plane, there are two alternatives:      

1. These two straight lines intersect (as shown in  Figure 1a),  and
2. These two straight lines do not intersect even at extended length
      (as shown in  Figure 1b).


Figure 1a. Intersecting
straight lines    


Figure 1b. Parallel
straight lines


      Definition
      Two straight lines in a plane are called  parallel  if they do not intersect
      even at extended length.

The next statement is a  postulate,  that is a statement, which is accepted without proof:
For a given straight line and a point in the plane outside of this straight line there is   
one and only one straight line parallel to the given straight line and passing through the
given point
.



Figure 2. The unique parallel
straight line passing through
the given point out the line

Theorem
If a straight line  a  is parallel to a straight line  b  and a straight line  b  is parallel to a straight line  c,
then the straight lines  a  and  c  are parallel.

Proof
Let us suppose that straight lines  a  and  c  are not parallel.  Then they have an intersection point.  Let us denote as  C 
this intersection point of the straight lines  a  and  c.
Then we have two straight lines,  a  and  c,  passing through the point  C  and parallel to the straight line  b,  which is
impossible due to the  postulate  above.

See the lesson  Parallel lines  in this site.


RELATED QUESTIONS

If line P contains points A (–1, 4) and B (3, –5), line q is parallel to line P and line... (answered by Alan3354)
Line p is parallel to line q. If line p has a slope of 3, what is the slope of... (answered by jim_thompson5910)
Given: p is perpendicular to q q is parallel to r Prove: p is perpendicular (answered by linjackie99@yahoo.com)
write the equation of a line through (-p, q) that is parallel to the line 3x-4y=... (answered by jim_thompson5910)
line p is parallel to the line x= -2. What is the slope of line... (answered by fractalier)
is the lines through points P(4,-7)and Q(3,-4) parallel to the line through points... (answered by mananth)
given: triangle ABC, median of line CM is extended to point P so that line CM is... (answered by richwmiller)
Prove that pq and rs are parallel line if p(1,5) q(4,2) r(1,9)... (answered by ikleyn)
Given: Line AEB and Line CED bisect each other at E Prove: Line AC is parallel to Line (answered by Mathtut)