### 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°).

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**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'

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**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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