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are equal. Construct a parallel line is the method to maintain the constant distance between the two lines so that they will

never meet. Parallel Lines are constructed by the help of geometry rules. It can be constructed using scale, pencil and

compass.

Condition of parallel lines slope of first line m1 = slope of second line m2

Now we will see some examples in which we will proof those two lines are parallel.

Proof that the above two lines (if constructed) are parallel

So the slope of first line is, m1 = (y2-y1)/ (x2-x1) = (12-4)/ (8 – 4) = 8/4 = 2

Therefore m1 = 2

Also given, another line passes through (2, 2) and (8, 14)

Therefore the slope of second line is, m2 = (y2-y1)/ (x2-x1) = (14-2)/ (8-2) = 12/6 = 2

Therefore m2 = 2.

Since slope of the two lines are equal that is m1 = m2 =2

Proof that the above two lines (if constructed) are parallel

So the slope of first line is, m1 = (y2-y1)/ (x2-x1) = (6-2)/ (4 – 2) = 4/2 = 2

Therefore m1 = 2

Also given, another line passes through (3, 3) and (6, 9)

Therefore the slope of second line is, m2 = (y2-y1)/ (x2-x1) = (9-3)/ (6-3) = 6/3 = 2

Therefore m2 = 2

Since slope of the two lines are equal that is m1 = m2 =2