# What is a Transversal Line? - Angles & Examples

## What is a Transversal?

A **transversal** is a line that cuts across two or more lines in the same plane. The transversal creates very distinct angle relationships when it crosses the other lines. Let's take a look at these angles that are created when the lines that are crossed are parallel.

### Transversal on Parallel Lines

When the transversal crosses a pair of **parallel lines**, lines that remain the same distance from each other, eight special angles are formed.

A real-life example of a transversal line would be a street cutting across railroad tracks. Since the railroad tracks will remain the same distance apart, the angles will have orderly relationships and many of them will be congruent. The congruent angles are created because of the equal distance between the parallel lines.

### Transversal on Non-Parallel Lines

When a transversal cuts across non-parallel lines, some of the special angles will exist like with parallel lines, but not all of them. The distance between the non-parallel lines will change the angle measurements.

## What Is a Transversal?

A **transversal** is two parallel lines intersected by a third line at an angle. The third line is referred to as the transversal line. When this line happens, several angles are created. You can use these angles to find the measurements of other angles. When using transversals in geometry you can think about puzzle pieces fitting together.

## What is a Transversal Angle?

A **transversal angle** is an angle created when a transversal line cuts across a pair of parallel lines. The transversal creates eight angles with the parallel lines. Let's take a look back at the diagram and break down the relationships between the angles.

The angles can be placed into two groups based on their angle measures. The groups are based on congruency. In the diagram, angles 1, 4, 5, and 8 are congruent. The other group of congruent angles is angles 2, 3, 6, and 7. The two groups will have different measures unless the transversal is perpendicular to the parallel lines. With visual inspection we can see that the angles within each group are congruent.

The angles can be also be grouped based on their location on the transversal and the parallel lines.

**Corresponding Angles**are a pair of angles that are on the same side of the transversal, one interior, one exterior, and are congruent. In the diagram the following pairs are corresponding angles: 1 & 5, 2 & 6, 3 & 7, and 4 & 8.**Consecutive Interior Angles**are a pair of angles on the same side of the transversal and between the parallel lines. They are supplementary angles. In the diagram the following pairs are consecutive interior angles: 3 & 5 and 4 & 6.**Alternate Interior Angles**are a pair of non-adjacent angles on the opposite sides of the transversal, between the parallel lines, and are congruent angles. Angles 3 & 6 and 4 & 5 are alternate interior angles.**Alternate Exterior Angles**are a pair of angles on the opposite side of the transversal, outside of the parallel lines, and are congruent angles. The alternate exterior angles are 1 & 8 and 2 & 7.

The transversal cutting across a pair of parallel lines will also create pairs of supplementary angles. These supplementary angles can be found inside and outside of the parallel lines. In the following diagram there are 2 pairs of **co-interior angles**. The pairs of angles are on the same side of the transversal, inside the parallel lines, and supplementary. In the diagram, angles D & F are a pair and angles C & E are the other pair.

We can tell the angles are supplementary because together they make half of a circle, which is {eq}180^\circ {/eq}.

**Co-exterior angles** are also on the same side of the transversal. They, too, are supplementary but are on the outside of the parallel lines. In the diagram angles B & H are a pair and angles A & G are the other pair of co-exterior angles.

## Examples of a Transversal

There are several examples of transversals. The road crossing the railroad tracks is one example. The railroad tracks are parallel lines.

Another example is a fence post crossing barbed wire. The barbed wires are parallel lines.

Some ladders also represent a transversal cutting across parallel lines. A step on the ladder can be viewed as a transversal going through the two parallel rails.

Note that with the steps of the ladder, the fence post crossing the barbed wire, and the road crossing the railroad tracks, we have transversal lines that are perpendicular to their respective parallel lines. Perpendicular transversal lines tend to be the norm in real-world examples, at least those constructed by humans. When the transversal is perpendicular to its parallel lines, all eight angles formed are congruent with each angle measuring 90 degrees.

## Lesson Summary

A **transversal** is a line that cuts across two or more lines in the same plane.

**Parallel lines** (lines that remain the same distance from each other) create eight special angles when cut by a transversal.

The eight angles created by a transversal and parallel lines are generally called **transversal angles**.

The eight angles can be grouped into two groups based on congruency.

There are a few other ways to group the angles based on distinct relationships:

**Corresponding Angles**are a pair of angles that are on the same side of the transversal, one interior and one exterior, and are congruent.**Consecutive Interior Angles**are a pair of angles on the same side of the transversal, between the parallel lines, and are supplementary angles.**Alternate Interior Angles**are a pair of angles on the opposite side of the transversal between the parallel lines and are non-adjacent congruent angles.**Alternate Exterior Angles**are a pair of angles on the opposite side of the transversal, outside of the parallel lines, and are congruent angles.**Co-interior angles**are a pair of angles on the same side of the transversal, inside the parallel lines, and are supplementary.**Co-exterior angles**are a pair of angles on the same side of the transversal and are supplementary but are on the outside of the parallel lines.

A transversal line and a pair of parallel lines can be thought of as a puzzle. The angles are all of the puzzle pieces and their relationships are what put them together.

## Angles

There are eight different angles in a transversal. They are placed into five different categories. Knowing these angles can help you solve many geometric problems.

### Supplementary Angles

**Supplementary angles** are pairs of angles that add up to 180 degrees. If you put two supplementary angle pieces together, you can draw a straight line across the top of the two angles. In essence, the two angles together make a half circle. Supplementary angles are not limited to transversals.

In this example, the supplementary angles are AB, CD, EF, GH and AC, BD, EG, FH.

### Interior Angles

**Interior angles** are angles that are on the inside of the two parallel lines. In the example, the interior angles are angles C, D, E, and F.

### Exterior Angles

**Exterior angles** are angles that are on the outside of the two parallel lines. In the example, the exterior angles are angles A, B, G, and H.

### Corresponding Angles

**Corresponding angles** are two angles that appear on the same side of the transversal line. One of the angles must be an interior angle and the other must be an exterior angle. Corresponding angles are congruent, meaning that they are equal measurements.

In the example, the corresponding angles are BF, DH, CG, and AE.

### Alternating Angles

**Alternating angles** are two angles that appear on alternate sides of the transversal line. The angles are either both interior or both exterior. Alternating angles are congruent, meaning that they are equal measurements, or are angled at the same degree.

In the example, the alternating angles are angles CF, ED, AH, and BG.

## Lesson Summary

**Transversals** are lines that intersect two parallel lines at an angle. Transversals contain eight separate angles that are categorized into five different categories: supplementary, interior, exterior, corresponding, and alternating. **Supplementary angles** add up to 180 degrees, **interior angles** appear inside the parallel lines, **exterior angles** appear outside the parallel lines, **corresponding angles** are on the same side of the transversal and are interior and exterior angles, and **alternate angles** are either both interior or both exterior and appear on alternate sides of the transversal. Finally, corresponding and alternating angles are congruent, meaning that they have the same measurement.

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## What Is a Transversal?

A **transversal** is two parallel lines intersected by a third line at an angle. The third line is referred to as the transversal line. When this line happens, several angles are created. You can use these angles to find the measurements of other angles. When using transversals in geometry you can think about puzzle pieces fitting together.

## Angles

There are eight different angles in a transversal. They are placed into five different categories. Knowing these angles can help you solve many geometric problems.

### Supplementary Angles

**Supplementary angles** are pairs of angles that add up to 180 degrees. If you put two supplementary angle pieces together, you can draw a straight line across the top of the two angles. In essence, the two angles together make a half circle. Supplementary angles are not limited to transversals.

In this example, the supplementary angles are AB, CD, EF, GH and AC, BD, EG, FH.

### Interior Angles

**Interior angles** are angles that are on the inside of the two parallel lines. In the example, the interior angles are angles C, D, E, and F.

### Exterior Angles

**Exterior angles** are angles that are on the outside of the two parallel lines. In the example, the exterior angles are angles A, B, G, and H.

### Corresponding Angles

**Corresponding angles** are two angles that appear on the same side of the transversal line. One of the angles must be an interior angle and the other must be an exterior angle. Corresponding angles are congruent, meaning that they are equal measurements.

In the example, the corresponding angles are BF, DH, CG, and AE.

### Alternating Angles

**Alternating angles** are two angles that appear on alternate sides of the transversal line. The angles are either both interior or both exterior. Alternating angles are congruent, meaning that they are equal measurements, or are angled at the same degree.

In the example, the alternating angles are angles CF, ED, AH, and BG.

## Lesson Summary

**Transversals** are lines that intersect two parallel lines at an angle. Transversals contain eight separate angles that are categorized into five different categories: supplementary, interior, exterior, corresponding, and alternating. **Supplementary angles** add up to 180 degrees, **interior angles** appear inside the parallel lines, **exterior angles** appear outside the parallel lines, **corresponding angles** are on the same side of the transversal and are interior and exterior angles, and **alternate angles** are either both interior or both exterior and appear on alternate sides of the transversal. Finally, corresponding and alternating angles are congruent, meaning that they have the same measurement.

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#### What's the definition of a transversal?

A transversal is a line that cuts across two or more lines in the same plane. The transversal creates very distinct angle relationships when it crosses the other lines.

#### What does transversal mean in angles?

A transversal angle is an angle created when a transversal line cuts across a pair of parallel lines. The transversal creates 8 distinct angles with the parallel lines.

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