Question

If two parallel lines are intersected by a transversal, then show that the bisectors of any pair of alternate interior angles are equal.

Class 9 Mathematics
Lines and Angles​

Answer 1

Answer:

hey mate...

your answer is..

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

Answer 2

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