1. GOAL 1 PROPERTIES OF PARALLEL LINES This section will require you to think about and use parallel lines. Although some of the theorems and ideas may seem obvious, you must always be ready to provide justification for any statements made. 3.3 PARALLEL LINES AND TRANSVERSALS

2. POSTULATE Corresponding Angles Postulate THEOREMS Alternate Interior Angles Consecutive Interior Angles Alternate Exterior Angles Perpendicular Transversal EXAMPLE 1

3. StatementsReasons 1. 2. 3. 4. 5. 6. Extra Example 1 Given Linear Pair Post. Substitution Given: Prove: 4 1 2 3 56 78 p q EXAMPLE 2

4. Extra Example 2 4 1 2 3 56 78 Given that find each measure. Give the postulate or theorem used. a. b. c. d. 70°;Linear Pair Postulate 70°;Corresponding Angles Postulate 110°; Alternate Exterior Angles Thm. or Linear Pair Postulate 70°; Alternate Exterior Angles Thm. or Linear Pair Postulate or Vertical Angles Theorem

5. Checkpoint EXAMPLE 3 AB DC 1 2 3 100° Extra Example 3 In the diagram above, how many angles have a measure of 100°? eight

6. GOAL 2 PROPERTIES OF SPECIAL PAIRS OF ANGLES EXAMPLE 4 3.3 PARALLEL LINES AND TRANSVERSALS

7. Extra Example 4 EXAMPLE 5 Use properties of parallel lines to find the value of x. 72° 1 (x – 8 )° Since by the Vertical Angles Theorem, and by the Consecutive Interior Angles Theorem, solve the equation:

8. Extra Example 5 Refer to Example 5. We now know that the diameter of Earth is about 7973 mi. Recalculate the distance between Syene and Alexandria using this figure. Using the equation from Example 5:

9. Checkpoint Use properties of parallel lines to find the value of x. (x – 20)° x°x° 70°m n x = 65

10. QUESTION: If a transversal is perpendicular to one of two parallel lines, what is the measure of all the angles formed? ANSWER: 90°