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The lines that do not intersect each other and have the same distance between them from any point of the lines are called parallel lines. In other words, parallel lines are non-intersecting lines having a constant distance. The railway tracks are the best example of parallel lines.
Let’s understand how to construct parallel lines with steps and examples using ruler and compass and using a ruler and set square.
Properties of Parallel Lines
The following are the main properties of parallel lines.
- The corresponding angles formed by parallel lines are equal.
- The vertically opposite angles formed by parallel lines are equal.
- The alternate interior angles formed by parallel lines are equal.
- The alternate exterior angles formed by parallel lines are equal.
- The pair of interior angles on the same side of the transversal are supplementary, that is they equal to $180^{\circ}$.
How to Construct Parallel Lines Through a Point Not Lying on a Given Line
You can use any one of the properties regarding the transversal and parallel lines to construct parallel lines using ruler and compasses only.
Steps to Construct Parallel Lines Through a Point Not Lying on a Given Line
The following steps are used to construct parallel lines through a point not lying on a given line.
Step 1: Take a line $l$ and a point $\text{A}$ outside $l$.
Step 2: Take any point $\text{B}$ on $l$ and join $\text{B}$ to $\text{A}$.
Step 3: With $\text{B}$ as centre and a convenient radius, draw an arc cutting $l$ at $\text{C}$ and $\text{BA}$ at $\text{D}$.
Step 4: Now with $\text{A}$ as centre and the same radius as in Step 3, draw an arc $\text{EF}$ cutting $\text{AB}$ at $\text{G}$.
Step 5: Place the pointed tip of the compass at $\text{C}$ and adjust the opening so that the pencil tip is at $\text{D}$.
Step 6: With the same opening as in Step 5 and with $\text{G}$ as centre, draw an arc cutting the arc $\text{EF}$ at $\text{H}$.
Step 7: Now, join $\text{AH}$ to draw a line $m$.
Line $m$ is parallel to the given line $l$.
Construction of Parallel Lines Using Set Square
You can also use a set square to construct parallel lines.
Steps for Construction of Parallel Lines Using Set Square
The following steps are used for the construction of parallel lines using set square.
Step 1: Position an edge of the set square against a ruler and draw a line along one of the other edges.
Step 2: Slide the set square into a new position while keeping the ruler fixed exactly at the same position.
Step 3: Draw a line along the same edge that was used in Step 1.
Line $l$ is parallel to line $m$, i.e, $l || m$
Practice Problems
- What are parallel lines?
- What are the properties of parallel lines?
- Which property of parallel lines is used to construct using a ruler and compass?
- Draw a line segment of 7.8 cm and then draw a line parallel to it.
FAQs
Can we construct parallel lines using a set square?
Yes, we can construct parallel lines using a set square. The steps involved are
Step 1: Position an edge of the set square against a ruler and draw a line along one of the other edges.
Step 2: Slide the set square into a new position while keeping the ruler fixed exactly at the same position.
Step 3: Draw a line along the same edge that was used in Step 1.
Which property of parallel lines is used to construct using a ruler and compass?
For constructing a line parallel to a given line we have to measure the inclination of the given angle with the reference and draw the same degree of inclination with the reference to get the line parallel to the given line.
Conclusion
The lines that do not intersect each other and have the same distance between them from any point of the lines are called parallel lines. The parallel lines can be constructed using a ruler and compass and also using a ruler and set square.
Recommended Reading
- How To Construct a Line Segment(With Steps & Examples)
- What are Collinear Points in Geometry – Definition, Properties & Examples
- What is a Transversal Line in Geometry – Definition, Properties & Examples
- What are Parallel Lines in Geometry – Definition, Properties & Examples
- What is Concurrent lines in Geometry – Definition, Conditions & Examples
- What is Half Line in Geometry – Definition, Properties & Examples
- What is a Perpendicular Line in Geometry – Definition, Properties & Examples
- Difference Between Axiom, Postulate and Theorem
- Lines in Geometry(Definition, Types & Examples)
- What Are 2D Shapes – Names, Definitions & Properties
- 3D Shapes – Definition, Properties & Types
