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Construction of Parallel Lines

# Construction of Parallel Lines

Two lines in a plane that never meet each other at any point are said to be parallel to each other.

Lesson Demo

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:

1. All pairs of alternate interior angles formed by parallel lines and a transversal are equal.

2. All pairs of corresponding angles formed by parallel lines and a transversal are equal.

3. All pairs of alternate exterior angles formed by parallel lines and a transversal are equal.

4. The interior angles formed on the same side of the transversal are supplementary (the sum of their measures is 1800).

#### Steps to construct parallel lines using the alternate interior angle property:

1. Draw a line, l.

2. Mark point A outside line l.

3. Mark point B on linel.

4. Draw line  joining points A and B.

5. Draw an arc with B as the centre, such that it intersects lines l and n at points Dand E, respectively.

6. Draw another arc with the same radius and A as the centre, such that it intersects line n at F.

7. Ensure that the arc drawn from A cuts line n between A and B.

8. Measure distance DE with the help of the compass.

9. Draw another arc with F as the centre and radius equal to DE.

10. Mark the point of intersection of this arc and the previous arc as G.

11. Draw line m passing through A and G.

12. Lines l and m are parallel.

#### Verification of the construction:

If the pair of alternate interior angles ∠ABC and ∠BAG are equal in measure, then line l //line m.
Hence, the construction is verified.

#### Steps to construct parallel lines using the corresponding angle property:

1. Draw line l and point P outside it.

2. Mark point Qon line l.

3. Draw line joining point P and point Q.

4. Draw an arc with Q as the centre, such that it intersects line l at R and line n at S.

5. Draw another arc with the same radius and P as the centre, such that it intersects line n at X.

6. Ensure that the arc drawn from P cuts line n outside QP.

7. Draw another arc withX as the centre and distance RS as the radius, such that it intersects the previous arc at Y.

8. Draw line m passing through points P and Y.

9. Lines l and m are parallel.

#### Verification of the construction:

If the pair of corresponding angles ∠PQR and ∠XPY are equal in measure, then lin l e II line m.