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.

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?

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

Can you identify each type of congruent
angle in the picture below?

Picture parallel lines cut by transversal
Alternate Interior Angles

$$\angle $$ 3 and $$\angle $$ 6
$$\angle $$ 4 and $$\angle $$ 5

Alternate Exterior Angles

$$\angle $$ 2 and $$\angle $$ 7
$$\angle $$ 1 and $$\angle $$ 8

Alternate Interior Angles

$$\angle $$ 1 and $$\angle $$ 5
$$\angle $$ 4 and $$\angle $$ 8
$$\angle $$ 2 and $$\angle $$ 6
$$\angle $$ 3 and $$\angle $$ 7

Line P is parallel to line v

Angles Formed by Parallel Lines and Transversal
Alternate Interior Angles

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

Angles Formed by Parallel Lines and Transversal
Alternate Exterior Angles

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

Angles Formed by Parallel Lines and Transversal
Identify the corresponding angles

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

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 interior

Interactive Parallel Line and Angles

Click and Drag Points E and F to explore the relationship of corresponding, alternate interior and alternate exterior angles that are formed by a transversal and parallel lines. (Full Size Version)

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