1 Lines Part 3 How to Prove Lines Parallel

Review Types of Lines –Parallel –Perpendicular –Skew Types of Angles –Corresponding –Alternate Interior –Alternate Exterior –Consecutive (same side) Interior –Consecutive (same side) Exterior –Vertical Angles –Linear Pair

Review of Conditional Statements Conditional Statement –Any statement in If…, then…format –Comprised of a hypothesis and a conclusion Converse –Interchanging the hypothesis and the conclusion of a conditional statement.

Example Hypothesis: Conclusion: Converse: Is the conditional statement true: Is the converse statement true:

Counterexample Counterexample: A verbal, geometric, or algebraic expression that is used to show that the statement is false. Original: Converse: Counterexample:

6 Proving Lines Parallel - Postulates & Theorems If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

7 Proving Lines Parallel - Postulates &Theorems If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

8 Proving Lines Parallel - Postulates &Theorems If two lines are cut by a transversal and consecutive interior angles are supplementary, then the lines are parallel.

9 Proving Lines Parallel - Postulates &Theorems If two lines are cut by a transversal and consecutive exterior angles are supplementary, then the lines are parallel.

10 Examples: Proving Lines Parallel Find the value of x which will make lines a and lines b parallel ° Answers: 1. 20°2. 50°3. 90°

11 Ways to Prove Two Lines Parallel Show that corresponding angles are equal. Show that alternative interior angles are equal. Show that consecutive interior angles are supplementary. Show that consecutive exterior angles are supplementary. In a plane, show that the lines are perpendicular to the same line.