Given :-

TO PROVE

PROOF

The arms of the angles may be parallel in the same sense or in the opposite sense.

So, three cases arise.

Case 1 :-

when both pairs of arms are parallel in same sence [ fig.( i ):

in the case , BA||ED and BC is transversal.

Again,

BC||EF and DE is transversal.

Case 2 :-

when both pairs of arms are parallel in opposite sence [ fig. (ii) ]

in this case, BA|| ED is the transversal

Again,FE ||BC and ED is transversal.

Case 3

When one pair of arms are parallel in same sense and other pair parallel in opposite sense: [Fig. (iii)]

In this case, A||ED and BC is the transversal.

Now, BC|| EF and DE is transversal