Question

We draw a line segment $PQ$ of length $5cm$. We take an external point $A$ of line segment. Let us draw paralel line through the point A to line segment PQ. [Let us draw three alternative process]

Answer 1

Method 1:
Steps of construction:
1. We draw a line segment $PQ$ of length $5cm$.
2. We take an external point A of line segment.
3. Draw an arc from A that intersects $PQ$ at two different points $B$ and $C$.
4. Draw perpendicular bisector of $BC$. It passes through A.
5. Draw perpendicular of this line through $A$.
6. This line is parallel to PQ.

Method 2:
Steps of Construction:
1. We draw a line segment $PQ$ of length $5cm$.
2. We take an external point A of line segment.
3. Draw a bigger arc from A cutting $PQ$ at a point.
4. Mark it as B.
5. With the same radius and $B$ as center, draw another arc on $PQ$ as $C$.
6.From $C$, with the same radius draw another arc cutting the first arc at $D$.
7. Join $D$ to $A$ and extend the line.
8. This line is parallel to $PQ$.

Method 3:
Steps of Construction:
1. We draw a line segment $PQ$ of length $5cm$.
2. We take an external point A of line segment.
3. We draw a transverse line passing through $A$ and cutting $PQ$ at $B$.
4. We draw the angle at $A$ equal to angle at $B$.
5. The corresponding drawn line is parallel to PQ.