1. Unit 1 Angles and Parallel Lines

2. Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal. When a transversal t intersects line n and m, eight angles of the following types are formed: Exterior angles Interior angles Consecutive interior angles Consecutive exterior angles Alternate exterior angles Alternate interior angles Corresponding angles tm n

3. Corresponding Angles Corresponding Angles: Two angles in the same position. These angles are congruent. 12 34 56 78

4. Alternate Interior Angles Alternate Interior Angles: Two angles that are on opposite sides of the transversal and inside the parallel lines. These angles are congruent. Circle 4 and 5 as an example of this type. 12 34 56 78

5. Alternate Exterior Angles Alternate Exterior Angles: Two angles that are on opposite sides of the transversal and outside the parallel lines. The angles are congruent. 12 34 56 78

6. Consecutive Interior Angles Consecutive Interior Angles: Two angles on the same side of the transversal and inside the parallel lines. These angles are supplementary (=180°). 12 34 56 78

7. Consecutive Exterior Angles Consecutive Exterior Angles: Two angles on the same side of the transversal and outside the parallel lines. These angles are supplementary (= 180°). 12 34 56 78

8. Vertical Angles Vertical Angles:Two angles that are across from each other. These angles are congruent. 12 34 56 78

9. Linear Pair Linear Pair: Supplementary angles that form a line (sum = 180  ) 12 34 56 78

10. Angles and Parallel Lines If two parallel lines are cut by a transversal, then the following pairs of angles are congruent. 1. Corresponding angles 2. Alternate interior angles 3. Alternate exterior angles If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary. 1. Consecutive interior angles 2. Consecutive exterior angles 3. Linear Pair

11. Example: If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers. m<2=80° m<3=100° m<4=80° m<5=100° m<6=80° m<7=100° m<8=80° m<9=100° m<10=80° m<11=100° m<12=80° m<13=100 ° m<14=80 ° m<15=100 ° m<16=80 ° t 16 15 1413 1211 10 9 8 7 65 34 2 1 s D C B A

12. Example: 1. the value of x, if m<3 = 4x + 6 and the m<11 = 126. If line AB is parallel to line CD and s is parallel to t, find: 2. the value of x, if m<1 = 100 and m<8 = 2x + 10. 3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20. ANSWERS: t 16 15 1413 1211 10 9 8 7 65 34 2 1 s D C B A 1. 30 2. 35 3. 33