if the arms of one angle are respectively parallel to the arms of another angle, show that the two angles are either equal or supplementary
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if the arms of one angle are respectively parallel to the arms of another angle, show that the two angles are either equal or supplementary
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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