Transversal
A transversal line passes through two lines in the same plane at two distinct points in the geometry. Transversals play a role in establishing the parallelism of two or more other straight lines in the Euclidean plane. A transversal intersects two lines at distinct points. Intersection caused by transversals forms several angles. These are corresponding angles, alternate interior angles, alternate exterior angles, and cointerior angles.
Transversals and Transverse Lines
For two or more straight lines, a transversal is any line that intersects two straight lines at distinct points. In the following figure, L_{1} and L_{2} are two lines that a transversal L cuts. Here, the L line is known as the transverse line. In the Universe of parallel and transverse lines, a transverse line connects the two parallel lines.
From the diagram, we can say that 'L is a transversal, cutting the lines L_{1} and L_{2}, and thus line L is the transversal line.
Constructing a Transversal with Parallel Lines
The construction of a transversal is easy. First, we create two parallel lines. We construct the angle (at which we want to create the transversal) on the first line (say x^{0}) as shown.
Further, we extend this constructed angle up to a point it covers both the parallel lines as done here. Here is what we get: Our transversal on the two parallel lines at the desired angle (x^{0}).
Transversal Angles
When a transversal cuts two parallel lines, several angles are formed by these two intersections. Those angles are given below:
 Corresponding angles
 Alternate Interior Angles
 Alternate Exterior Angles
 Cointerior Angles
From the given diagram, if we try to organize the angles based on the relative positions they occupy, we get the following categories of angles :
Corresponding Angles
The following pairs of angles are corresponding angles:
 ∠1 and ∠5
 ∠2 and ∠6
 ∠3 and ∠7
 ∠4 and ∠8
Alternate Interior Angles
The following pairs of angles are alternate interior angles:
 ∠3 and ∠6
 ∠4 and ∠5
Alternate Exterior Angles
The following pairs of angles are alternate exterior angles:
 ∠1 and ∠8
 ∠2 and ∠7
Cointerior Angles
The following pairs of angles are cointerior angles:
 ∠3 and ∠5
 ∠4 and ∠6
Important Notes:
 A transversal is any line that intersects two straight lines at distinct points.
 A transversal that cuts the lines L_{1} and L_{2} is the transversal line.
 Intersection caused by transversals forms several angles. These are :
a) Corresponding Angles
b) Alternate Interior Angles
c) Alternate Exterior Angles
d) Cointerior Angles
Challenging Questions

Two different transversals cut two parallel lines at distinguished points. All the corresponding angles formed by these four intersections are found to be equal. Can you comment upon the figure formed by these four lines? (Hint: Opposite angles of the formed quadrilateral are found to be equal in the given scenario)
Related Articles on Transversal
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Solved Examples on Transversal

Example 1: Consider the following figure, in which L_{1} and L_{2} are parallel line segments. What is the value of ∠C?
Solution: Through C, draw a line segment parallel to L_{1} and L_{2}, as shown below:
We have ∠x = ∠β = 60º (alternate interior angles) and ∠y = 180º – 120º (cointerior angles) ⇒ ∠y = 60º. Thus, we get ∠C = ∠x + ∠y = 120º. ∴ ∠C = 120º

Example 2: Consider the following figure, in which L_{1}, L_{2,} and L_{3} are parallel lines. The line AC is perpendicular to L_{3}, as shown. What are the values of ∠x, ∠y, and ∠z?
Solution: Since AC ⊥ L_{3}, it will be perpendicular to each of the other two parallels as well. This means that ∠x = 90º – 60º = 30º. Now, ∠y = 180º – ∠x (cointerior angles) ⇒ ∠y = 150º
Also, ∠z = ∠y = 150º (corresponding angles). ∴ ∠x = 30º^{ }& ∠z = ∠y = 150º

Example 3: Consider the following figure, in which L_{1}  L_{2}. The angle bisectors of ∠BAX and ∠ABY intersect at C, as shown. Find the value of ∠ACB.
Solution: We note that ∠BAX and ∠ABY are cointerior angles, which means that their sum is 180^{0 }⇒ ∠BAX + ∠ABY = 180º ⇒ 2(∠1 + ∠2) = 180º ⇒ ∠1 + ∠2 = 90º
Now, in ΔACB, we apply the angle sum property: ∠1 + ∠2 + ∠ACB = 180º ⇒ 90º + ∠ACB = 180º. ∴ ∠ACB = 90º
Practice Questions on Transversal
FAQs on Transversal
Can Transversal Lines be Straight?
Yes, transversals are straight lines that intersect two or more lines at different points.
How Many Angles are Formed by the Transversal?
The transversal forms several angles. Some of those angles are:
 Corresponding Angles
 Alternate Interior Angles
 Alternate Exterior Angles
 Cointerior Angles
What does Transversal mean in Geometry?
In geometry, a transversal is a line, ray, or line segment that intersects other lines, rays, or line segments on a plane at different intersecting points. When it intersects parallel lines, there formed several angles that share a common property, on the other hand when a transversal intersects two or more nonparallel lines, there is no relationship between the angles formed.
How Many Angles are Formed by the Transversal?
When two parallel lines are intersected by the transversal, eight angles are formed. The eight angles include corresponding angles, alternate interior and exterior angles, vertically opposite angles, and cointerior angles.
Are Vertical Angles Equal?
Vertical angles are always equal to each other in measure. When a transversal intersects a line, two pairs of vertical angles are formed.
Do Transversal Lines have to be Parallel?
No. Transversal lines can be at any angle to the given parallel lines. Thus, any 2 transversals need not be parallel.
What are Corresponding Angles in a Transversal?
Two or more angles that are on the same side of the transversal when it cuts two or more parallel lines, they are called corresponding angles. When a transversal intersects two parallel lines, four pairs of corresponding angles are formed.