Question

how to prove the lines parallel?

Answer 1

i) distance between the lines are constant
ii) the lines never intersects each other
iii) slope of the lines are equal
any one of these are true then the lines are parallel

Answer 2

◆ If lines are parallel then distance between any point on the line remains same.

if this conditions are not enough to prove then check angles:-

If....

1) Alternate angles are equal

2) corresponding angles are equal

3) sum of co-interior angles are supplementary.

=) in the given figure:-

if
/_1 = /_5 ( corresponding angles)

/_2 =/_6

similarly
/_4 = /_ 8

/_3 =/_7

all are pair of corresponding angles.

/_3 = /_5 ( Alternate angles)

/_2 = /_8. ( " " " " " " ". " " ")

and,
if
/_2 + /_5 =180

sum of co-interior angles

etc

if any given conditions are satisfied then we can say that lines are parallel.

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Hope it will help u