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Parallel Lines cut by a Transversal

Angles formed

What is a transversal?

Answer: A transversal is a line, like the red one below, that intersects two other lines.

transversal

Typically, the intercepted lines like line a and line b shown above above are parallel, but they do not have to be.

What is so special about a transversal?

Answer: When a transversal cuts (or intersects) parallel lines several pairs of congruent and supplementary angles are formed.

Interior and Exterior Regions

We divide the areas created by the parallel lines into an interior area and the exterior ones.
Interior
Interior Regions
Exterior
Exterior Regions
These regions are used in the names of the angle pairs shown next.

The Congruent Angle Pairs

There are 3 types of angles that are congruent: Alternate Interior, Alternate Exterior and Corresponding Angles.

Parallel Line Transversal Angle Picture

Can you make a Z?

A way to help identify the alternate interior angles.

Alternate Interior Angles Draw Letter Z

Some people find it helpful to use the 'Z test' for alternate interior angles.
If you can draw a Z or a 'Backwards Z' , then the alternate interior angles are the ones that are in the corners of the Z

Problem 1

Line $$\overline P $$ is parallel to line $$ \overline V $$

Parallel Lines and Transversal

Directions: Identify the alternate interior angles.

$$ \angle$$D and $$ \angle$$W
$$ \angle$$X and $$ \angle$$C

Alternate Interior Angles Formed by Parallel Lines and Transversal
Problem 2

Line $$\overline P $$ is parallel to line $$ \overline V $$

Parallel Lines and Transversal

Directions: Identify the alternate exterior angles.

$$ \angle$$A and $$ \angle$$Z
$$ \angle$$Y and $$ \angle$$B

Alternate Exterior Angles Formed by Parallel Lines and Transversal
Problem 3

Line $$\overline P $$ is parallel to line $$ \overline V $$

Parallel Lines and Transversal

Directions: Identify the corresponding angles.

$$ \angle$$A and $$ \angle$$W
$$ \angle$$D and $$ \angle$$Z
$$ \angle$$X and $$ \angle$$B
$$ \angle$$C and $$ \angle$$Y

Corresonding Angles Formed by Parallel Lines and Transversal

The Supplementary Angle Pairs

There are 2 types of supplementary angles that are formed: same side interior and same side exterior.

Same Side Interior
Same Side Interior
Same Side Exterior
Same Side Exterior

Interactive Parallel Line and Angles

Explore the rules for the different types of congruent and supplementary angles here by dragging the points and selecting which angle pair you'd like to explore.

You can create a customized shareable link (at bottom) that will remember the exact state of the app--which angles are selected and where the points are, so that you can share your it with others.


∠A 90 ∠W 90
∠B 90 ∠X 90
∠C 90 ∠Y 90
∠D 90 ∠Z 90
Drag Points Of The Lines To Start Demonstration

Back to Geometry Next to Parallel Lines Practice