Angle in Parallel Lines

Parallel lines are lines that never intersect (cross each other), no matter how far they extend. In other words, the distance between the two lines remains constant at every point along their lengths. When represented in a coordinate plane, parallel lines have the same slope.

A transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects parallel lines, it forms pairs of angles with important properties.

Alternate Angles

Alternate angles are formed on opposite sides of the transversal, and between the parallel lines. When two lines are parallel, their alternate angles are equal.

  • As a result, the lines form a Z shape, so they are often called Z angles

Corresponding Angles

Corresponding angles are angles that have the same position when two parallel lines are crossed by another line called a transversal. They are created where the transversal intersects each parallel line.

  • Therefore, the lines form an F pattern, this is why they are often called F angles

When lines are parallel, their corresponding angles are equal.

Co-Interior Angles

Co-interior angles are formed on the same side of the transversal and between the parallel lines. When lines are parallel, the sum of the interior angles on the same side of the transversal is 180°.

  • As a result, the lines form a C pattern, so they are often called C angles

All Angles in Parallel Lines

We’ve already looked at alternate angles, corresponding angles, and co-interior angles individually. Now, let’s look at how they all work together.

In the diagram below, two parallel lines are intersected by a transversal, creating a variety of angles.

  • Corresponding angles – These are angles in matching positions on both parallel lines. They are always equal to each other. Look for angles that seem to have the same location, but are on different parallel lines.
  • Alternate angles – These angles are found on opposite sides of the transversal and are between the two parallel lines. There are two pairs of alternate angles, with one angle in each pair being on the left side of the transversal and one on the right side. In each pair, the angles are equal.
  • Co-interior angles – These angles are located between the parallel lines and share a common side with the transversal. There are two pairs of co-interior angles, with one on each side of the transversal. The angles in each pair add up to 180°.

Notice how the angles are either equal or add up to 180° based on their position and relationship to the transversal and parallel lines.

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