# Construct Parallel Lines

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Parallel lines are the lines which never intersect. Construct parallel line means we have to construct two lines whose slope

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.

Example 1:- One line passes through the point (4, 4) and (8, 12) and another line passes through the point (2, 2) and (8, 14).

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

Solution: Given One line passes through (4, 4) and (8, 12)

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

Therefore the two lines are parallel.

Example 2:- One line passes through the point (2, 2) and (4, 6) and another line passes through the point (3, 3) and (6, 9).

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

Solution: Given One line passes through (2, 2) and (4, 6)

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

Therefore the two lines are parallel.