(8) ff 2 parallel lines are In to by a
transversal, then prove that the bisectors of 2
atbernate angles
are Parallel
Answers
Answer: According to the question :-
⇒ It is already given that a transversal intersects two parallel lines
⇒ We need to prove that bisctors of the alternate interior angles are parallel .......
→ (i.e - GL is parallel to HM)
PROOF :-
⇒ It is already given in the figure that EF is transversal , and AB and CD is parallel to one another .
⇒So , ∠ GHD = ∠ EGB ( Interior angle on the same side of the transversal )
⇒ Also ,
\frac{1}{2}\ \textless \ GHD= \frac{1}{2}\ \textless \ EGB
⇒ Hence we get ∠ MHD = ∠ LGB
→ Well , These are the angles which are formed by the line GL and Hm.....
→ Therefore it is proved that GL and HM are parallel
∴ GL || HM