What is a Transversal Line in Geometry – Definition, Properties & Examples

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There are various types of lines that you study in geometry such as parallel lines, perpendicular lines, half lines, concurrent lines, etc. Transversal lines are also one such type of special line, that are widely studied along with parallel lines. There are numerous real-life examples of transversal lines that can be found such as a road crossing two or more roads, or a railway line crossing several other lines.

Let’s understand what is a transversal line in geometry and its properties with examples.

What is a Transversal Line in Geometry?

In geometry, a transversal is any line that intersects two straight lines at two distinct points. Consider two straight lines $l_1$ and $l_2$, and $t$ is a transversal line. The transversal $t$ cuts (or intersects) the two lines $l_1$ and $l_2$ at two distinct points.

In the above figure, we observe that $t$ is a transversal, cutting the lines $l_1$ and $l_2$, and thus line $t$ is the transversal line. Here, there is no relationship between the angles formed as the lines are not parallel.

Angles Formed By Transversal Line

After understanding what is a transversal line in geometry, let’s understand about different types of angles formed by a transversal line. Whenever a pair of parallel lines is intersected by a transversal line, eight angles are formed. The angles made by a transversal can be categorized into the following types 

• Corresponding angles
• Vertically opposite angles 
• Alternate interior angles 
• Alternate exterior angles 
• Interior angles on the same side of the transversal or co-interior angles

Let’s now understand what these angles are.

Corresponding Angles

Corresponding angles are formed on the same side of the transversal.

In the above figure, the pairs of corresponding angles are

• $\angle 1$ & $\angle 5$
• $\angle 2$ & $\angle 6$
• $\angle 3$ & $\angle 7$
• $\angle 4$ & $\angle 8$

Vertically Opposite Angles

Vertically opposite angles are formed when two straight lines intersect each other and they are equal in measure.

In the above figure, the pairs of vertically opposite angles are

• $\angle 1$ & $\angle 3$
• $\angle 2$ & $\angle 4$
• $\angle 5$ & $\angle 7$
• $\angle 6$ & $\angle 8$

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines that are intersected by a transversal.

In the above figure, the pairs of alternate interior angles are

• $\angle 3$ & $\angle 5$ 
• $\angle 4$ & $\angle 6$

Alternate Exterior Angles

Alternate exterior angles are formed on either side of the transversal.

In the above figure, the pairs of alternate exterior angles are

• $\angle 1$ & $\angle 7$
• $\angle 2$ & $\angle 8$

Interior Angles on the Same Side of the Transversal or Co-Interior Angles

Interior angles on the same side of the transversal or co-interior angles are formed on the inside of the transversal.

In the above figure, the pairs of interior angles on the same side of the transversal or co-interior angles are

• $\angle 3$ & $\angle 6$
• $\angle 4$ & $\angle 5$

Note: The above pairs of angles are used to check whether the given pair of lines are parallel or not. For detail check here.

Practice Problems

1. What is meant by a transversal line in geometry?
2. At how many points, does a transversal intersects
   • two parallel lines
   • three parallel lines
3. How many angles are formed by a transversal when it intersects
   • two parallel lines
   • three parallel lines
4. Define the following with respect to a pair of lines and a transversal
   • Corresponding angles
   • Vertically opposite angles 
   • Alternate interior angles 
   • Alternate exterior angles 
   • Interior angles on the same side of the transversal or co-interior angles

FAQs

Conclusion

In geometry, a transversal is any line that intersects two straight lines at two distinct points. In such cases, eight angles are formed which are categorized as corresponding angles, vertically opposite angles, alternate interior angles alternate exterior angles, and interior angles on the same side of the transversal or co-interior angles.

Recommended Reading

• 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