Q. 24.4( 13 Votes )

In Fig. 6.10, 1 = 60° and 6 = 120°. Show that the lines m and n are parallel.


Answer :

It is given to us –


1 = 60°


6 = 120°


We have to show that m and n are parallel to each other.


We can see that l is a ray standing on the line m. So, by linear pair axiom,


1 + 4 = 180°


60° + 4 = 180°


4 = 180° - 60°


4 = 120° - - - - (i)


Similarly,


1 + 2 = 180°


60° + 2 = 180°


2 = 180° - 60°


2 = 120° - - - - (ii)


Again, 2 + 3 = 180°


120° + 3 = 180°


3 = 180° - 120°


3 = 60° - - - - (iii)


Since, 6 = 120° and 2 = 120° [from equation (ii)],


We can say that these corresponding angles are equal, i.e.,


6 = 2 = 120° - - - - (iv)


We can say that l is a ray standing on the line n. By linear pair axiom,


6 + 5 = 180°


120° + 5 = 180°


5 = 180° - 120°


5 = 60° - - - - (v)


Since, 1 = 60° and 5 = 60° [from equation (v)],


We can say that these corresponding angles are equal, i.e.,


1 = 5 = 60° - - - - (vi)


Similarly, we get


8 = 4 = 120° (which are also the corresponding angles, and from equation (i), 4 = 120°)


And, 7 = 3 = 60° (which are also the corresponding angles, and from equation (iii), we have 3 = 60°)


Thus, we can say that


l is a transversal intersecting two lines m and n such that each pair of corresponding angles are equal.


Then, lines m and n are parallel to each other.


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