2. 3/16/20161 LESSON 2.G PROPERTIES OF PARALLEL LINES During today’s lesson, you will prove properties of parallel lines cut by a transversal.

3. Postulate: Alternate Interior Angles Postulate If two lines are cut by a transversal, then the alternate interior angles which are formed are _________________. ll lines  alternate interior angles  Recall, a postulate is a statement which we accept as being true. 3/16/20162

4. If two lines are cut by a transversal, then the corresponding angles which are formed are congruent. Given: r // s r Prove:  1   4 s 3/16/20163 4 3 1 Labeled Diagram: Given:Prove: STATEMENTSREASONS 1. 2. 3. 4. 5. 6. // lines  corresponding angles 

5. If two lines are cut by a transversal, then the same- side interior angles which are formed are supplementary 3/16/20164 1 2 3

6. 3/16/20165 st u v 3 4 5 Given: s // t ; u // v Prove:  3   5 Statements Reasons 1. s //t ; u //v 1. Given 2.  3   4 3.  4   5 3. // lines  corres.  ’s  2. // lines  corres.  ’s  4.  3   5 4. Trans. Prop.  Example 1:

7. 3/16/20166 Example #2 l m d b e ac The sum of the measures of the interior angles of any triangle is 180. Given: l || m. Prove: m  a + m  b + + m  c = 180

8. 3/16/20167 StatementsReasons

9. 3/16/20168 Guided Practice: Now, it’s your turn! pq l m 7 5 1 3 24 68 Given: l || m and p || q. Prove:  8   2 Given: l || m and p || q. Prove:  7   2 Given: l || m and p || q. Prove: m  4 + m  3 = 180 Given: l || m and p || q. Prove: m  7 + m  3 = 180 42 

10. 3/16/20169 HOMEWORK ASSIGNMENT