Parallel Lines and Transversals Angle

When two parallel lines or normal lines are intersected by another line, then it is called a transversal. The transversal line is the one that intersects these lines. An example below can explain this further.

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In this example above, you can see there are three different lines. Line A and Line B are two normal lines on a plane surface. They are not parallel. Line P intersects these two lines, Line A and Line B, and this line is called the transversal line. 

The example below shall explain this further.

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As you can see from the image above, Line A and Line B are parallel to each other. They are equidistant to each other. Line P, which crosses the two lines, is the transversal line.

Moving forward, these lines with transversal intersecting create several angles. This article shall study different angles that are created with parallel lines intersected by the transversal lines.  

Parallel Lines

Two lines are called parallel to each when the distance between them remains constant, equidistant, and they do not meet at any point. Therefore, a parallel line goes up to a long-distance as they never intersect or meet each other. Moreover, parallel lines move in the same direction.

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In the example above, line A is parallel to line B as they are at an equal distance and do not meet or intersect.

1. Transversal Angles

When two parallel lines are intersected by a line, transversal line, the angle at which it intersects is called a transversal angle. Eight angles, four pairs, are produced due to the intersection of two parallels by a transversal line. 

The different types of transversal angles are vertically opposite angles, corresponding angles, alternate interior angles, alternate exterior angles, and interior angles on the same side of the transversal line.

2. Vertically Opposite Angle

The vertically opposite angles exist in a pair. These angles are opposite to each other when a transverse line crosses parallel lines. Moreover, they are equal in value. An example of the vertically opposite angle is given below:

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∠x = ∠y, in the case of parallel lines.

The ∠x and ∠y are a pair of vertically opposite angle and there are equal in value when parallel lines are intersected by a transversal line. 

3. Corresponding Angles

Corresponding angles are those which occupy the same position at each intersection of the transversal line. Moreover, these angles are equal in the cases when the transversal intersects two or more parallel lines. The example below shall explain this further.

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∠x = ∠y, in the case of parallel lines.

In the example below, you can observe the intersection points are the same and therefore the corresponding angles are created at those points. Similar to vertically opposite angles, when a transverse intersects a set of parallel lines, then the corresponding angles are equal in value.

4. Alternate Interior Angle

Another pair of angles observed in the parallel lines crossed by a transversal line. The exists on the inner side and at the opposite position of the transversal line. The example below elucidates this further.

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∠x = ∠y, in the case of parallel lines.

The diagram depicts the position of the alternate interior angle. They exist on the inner side of the parallel line and are on the opposite side of the transversal line. In the case of parallel lines, they are equal to each other. 

5. Alternate Exterior Angle

Similar to the alternate interior angle, the alternate exterior angle exists in pairs. Instead of the inner position, as the name suggests these angles are on the exterior part of the parallel lines and on the alternate side of the transversal line. This diagram below shall explain this further. 

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∠x = ∠y, in the case of parallel lines.

The diagram above explains the positioning of the exterior alternate angle. They are similar to interior alternate angles with a minor difference in terms of positioning. Again, in the case of parallel lines, they are equal to each other. 

Interior Angle on the Same Side of the Transversal Line

As the name suggests, these angles exist on the same side of the transversal line and are found on the inner side. The position of these angles can be better understood using a diagram which is mentioned below.

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In the diagram above, ∠x and ∠y are supplementary in nature and therefore the summation of these is 180o. The line has to be parallel, for these interior angles to be supplementary in nature.

The parallel line when intersected by a transversal line, can lead to different angles. The five main categories of these angles are vertically opposite angles, corresponding angles, alternate interior angles, alternate exterior angles, and interior angles on the same side of the transversal line. 

The value of these different angles can be easily calculated if the value of one of them is available.