# Parallel and Perpendicular Lines

# Euclid's Parallel Postulate Exercises

### Example 1

Express m∠*F* in terms of m∠*Y*.

### Example 2

Out of the alternate interior angles theorem, the corresponding angles theorem, and the alternate exterior angles theorem, which one is disproved by the parallel postulate?

### Example 3

What are the values of *m* and *n*?

### Example 4

Are lines *a* and *b* parallel if *p* = 13 and *q* = 54?

### Example 5

In what branch of geometry is the parallel postulate false?