Question

if the bisector of a pairs of all angles formad by a transversal with two given lines are parallel, prove that lines are parallel.

Answer 1

$\textbf{ Hello Mate! }$

$\textbf{ Given }$ : OX || MY and OX and MY are angle bisectors.

$\textbf{ To prove }$ : AB || CD

$\textbf{ Proof }$ :

Since, OX || MY

< 1 = < 2 [ Alternate angles ]

On multiplying equation by 2

2< 1 = 2< 2

< AOM = < OMD [ Given ]

Thus, alternate angles formed by transversal are equal hence, AB || CD

$\boxed{ \textsf{ \red{ Hence\:proved }}}$

Have great future ahead!