Parallel Line Theorems and Converse

Corresponding Angle Postulate Converse

• If two parallel lines are cut by a traversal, then corresponding angles are supplementary.

• If two parallel lines are cut by a traversal, then corresponding angles are congruent.

• If corresponding angles are congruent, then two parallel lines are cut by a traversal.

• If corresponding angles are supplementary, then two parallel lines are cut by a traversal.

Alternate Interior Angles Theorem Converse

• If a pair of parallel lines is cut by a traversal, then alternate interior angles are supplementary.

• If a pair of parallel lines is cut by a traversal, then alternate interior angles are congruent.

• If alternate interior angles are congruent, then a pair of parallel lines is cut by a traversal.

• If alternate interior angles are supplementary, then a pair of parallel lines is cut by a traversal.

Consecutive Interior Angles Theorem Converse

• If a pair of parallel lines is cut by a traversal, then consecutive interior angles are supplementary.

• If a pair of parallel lines is cut by a traversal, then consecutive interior angles are congruent.

• If consecutive interior angles are congruent, then a pair of parallel lines is cut by a traversal.

• If consecutive interior angles are supplementary, then a pair of parallel lines is cut by a traversal.

Consecutive Exterior Angles Theorem Converse

• If a pair of parallel lines is cut by a traversal, then consecutive exterior angles are supplementary.

• If a pair of parallel lines is cut by a traversal, then consecutive exterior angles are congruent.

• If consecutive exterior angles are congruent, then a pair of parallel lines is cut by a traversal.

• If consecutive exterior angles are supplementary, then a pair of parallel lines is cut by a traversal.

• Not valid

• Alternate interior angles theorem

• Alternate interior angles converse

• Consecutive interior angles theorem

• Consecutive interior angles converse

What is the value of x?

• 60

• 70

• 150

• 330

What is the value of c?

• 140

• 40

• 220

• 20

What is the value of b?

• 80

• 90

• 170

• 350

How can we describe these angles?

• Corresponding angles

• Alternate angles

• Interior angles

• Vertically opposite angles

What is the size of angle x?

• 108

• 72

• 288

• 198