In Fig.6.6, which of the two lines are parallel and why?


In the 1st figure –


Let the intersecting points of l and n be a, and of m and n be b respectively.


We have, lab = 132°, abm = 48° - - - - (i)


l is a ray on the line n. By linear pair axiom,


nal + lab = 180°


nal + 132° = 180°


nal = 180° - 132°


nal = 48° - - - - (ii)


Also, we have abm = 48° from equation (i)


We can say that, the two corresponding angles,


abm = nal = 48° - - - - (iii)


Since, the two corresponding angles are equal, such that a transversal n intersects two lines, then they are parallel to each other.


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