# 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.

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.

#### Can you make a 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?

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

Alternate Interior Angles

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

Alternate Exterior Angles

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

Identify the corresponding angles

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

### 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 Exterior

### 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)

### Ultimate Math Solver (Free)

Free Algebra Solver ... type anything in there!