If two lines are parallel then prove that any pair of bisictors of thier alternate interior angle is also parallel.

Asked by amarjitruksh | 20th Jun, 2022, 10:40: PM

Expert Answer:

Let AB and CD be the two paralle lines and XY be their transverval intersecting AB at X and CD at Y
 
Since alternate angles are equal
Therefore, angle BXY = angle DYX
Therefore, 2a = 2b
i.e. a = b
So, for lines XP and YQ, angle PXY = angle QYX
Thus, lines PX and QY are parallel

Answered by Renu Varma | 25th Jun, 2022, 12:12: PM