# Construction of Parallel Lines : Mathematics

### Construction of Parallel Lines : Mathematics NCERT / CBSE Revision Notes

Two lines in a plane that never meet each other at any point are said to be parallel to each other.
Any line intersecting a pair of parallel lines is called a transversal.

Properties of angles formed by parallel lines and transversal:
• All pairs of alternate interior angles are equal.
• All pairs of corresponding angles are equal.
• All pairs of alternate exterior angles are equal.
• The interior angles formed on the same side of the transversal are supplementary (the sum of their measures is 180°).

Steps to construct parallel lines using the alternate interior angle property:
Step 1: Draw line 'l' and point A outside it.
Step 2: Mark point B on line 'l'.
Step 3: Draw line 'n' joining point A and point B.
Step 4: Draw an arc with B as the centre, such that it intersects line 'l' at D and line 'n' at E.
Step 5: Draw another arc with the same radius and A as the centre, such that it intersects line 'n' at F.  Ensure that arc drawn from A cuts the line 'n' between A and B.
Step 6: Draw another arc with F as the centre and distance DE as the radius.
Step 7: Mark the point of intersection of this arc and the previous arc as G.
Step 8: Draw line 'm' passing through points A and G.

Line 'm' is the required parallel line.
Verification of the construction
If the pair of alternate interior angles are equal in measure, then line 'l' is parallel to line 'm'.

Steps to construct parallel lines using the corresponding angle property
Step 1: Draw line 'l' and point P outside it.
Step 2: Mark point Q on line 'l'.
Step 3: Draw line 'n' joining point P and point Q.
Step 4: Draw an arc with Q as the centre, such that it intersects line 'l' at R and line 'n' at S.
Step 5: Draw another arc with the same radius and P as the centre, such that it intersects line 'n' at X.  Ensure that arc drawn from P cuts the line 'n' outside QP.
Step 6: Draw another arc with X as the centre and distance RS as the radius, such that it intersects the previous at Y.
Step 7: Draw line 'm' passing through points P and Y.

Line 'm' is the required parallel line.
Verification of the construction
If the pair of corresponding angles are equal in measure, then line 'l' is parallel to line 'm'.

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