What is a transversal?
Answer: A transversal is a line, like the red one below, that intersects two other lines.
![transversal](images/transversal/transversal.jpg)
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
![Interior Regions](images/transversal/angles/interior-regions-parallel-ln-transversal.png)
![Exterior Regions](images/transversal/angles/exterior-regions-parallel-ln-transversal.png)
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](images/transversal/angles/picture-of-parallel-lines-transversal-angles-v2.png)
Can you make a Z?
A way to help identify the alternate interior angles.
![Alternate Interior Angles Draw Letter Z](images/transversal/angles/alternate-interiors-draw-a-z-v2.png)
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
$$ \angle$$D and $$ \angle$$W
$$ \angle$$X and $$ \angle$$C
![Alternate Interior Angles Formed by Parallel Lines and Transversal](images/transversal/angles/alternate-interior-angles-color-coded-v2.png)
Problem 2
$$ \angle$$A and $$ \angle$$Z
$$ \angle$$Y and $$ \angle$$B
![Alternate Exterior Angles Formed by Parallel Lines and Transversal](images/transversal/angles/alternate-exterior-angles-color-coded-v2.png)
Problem 3
$$ \angle$$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](images/transversal/angles/corresponding-angles-color-coded-v2.png)
The Supplementary Angle Pairs
There are 2 types of supplementary angles that are formed: same side interior and same side exterior.
![Same Side Interior](images/transversal/angles/same-side-interior-color-coded-v2.png)
![Same Side Exterior](images/transversal/angles/same-side-exterior-color-coded-v2.png)
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 |