1. 9/29/15 Unit 2: Parallel Lines Aim: Students will be able to identify relationships between angles formed by two parallel lines cut by a transversal Homework: Do Now: Solve for x and y

2. Parallel Lines and Transversals You will learn to identify the relationships among pairs of interior and exterior angles formed by two parallel lines and a transversal.

3. Parallel Lines and Transversals In geometry, a line, line segment, or ray that intersects two or more lines at different points is called a __________ transversal l m B A is an example of a transversal. It intercepts lines l and m. Note all of the different angles formed at the points of intersection. 1 2 34 5 7 6 8

4. Parallel Lines and Transversals Definition of Transversal In a plane, a line is a transversal if it intersects two or more lines, each at a different point. The lines cut by a transversal may or may not be parallel. l m 1 2 3 4 5 7 6 8 Parallel Lines t is a transversal for l and m. t 1 2 3 4 5 7 6 8 b c Nonparallel Lines r is a transversal for b and c. r

5. Parallel Lines and Transversals Two lines divide the plane into three regions. The region between the lines is referred to as the interior. The two regions not between the lines is referred to as the exterior. Exterior Interior

6. l m 1 2 3 4 5 7 6 8 Parallel Lines and Transversals When a transversal intersects two lines, _____ angles are formed. eight These angles are given special names. t Interior angles lie between the two lines. Exterior angles lie outside the two lines. Alternate Interior angles are on the opposite sides of the transversal, between the lines. Same Side Interior angles are on the same side of the transversal, between the lines. Alternate Exterior angles are on the opposite sides of the transversal, outside the lines. Same Side Exterior angles are on the same side of the transversal, outside the lines. Alternate angles lie on opposite sides of the transversal Same Side angles lie on the same side of the transversal

7. Parallel Lines and Transversals Alternate Interior Angles AIA If two parallel lines are cut by a transversal, then each pair of Alternate interior angles is _________. 1 2 3 4 5 7 6 8 congruent

8. Parallel Lines and Transversals 1 2 3 4 5 7 6 8 Same Side Interior Angles SSI If two parallel lines are cut by a transversal, then each pair of Same side interior angles is _____________. supplementary

9. Same Side Exterior Angles SSE If two parallel lines are cut by a transversal, then each pair of Same side exterior angles is _____________. Parallel Lines and Transversals 1 2 3 4 5 7 6 8 supplementary

10. Parallel Lines and Transversals 1 2 3 4 5 7 6 8 Alternate Exterior Angles AEA If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is _________. congruent

11. Corresponding Angles CA If two parallel lines are cut by a transversal, then each pair of corresponding angles is _________. congruent Parallel Lines and Transversals

12. Parallel Lines w/a transversal AND Angle Pair Relationships Concept Summary CongruentSupplementary alternate interior angles- AIA alternate exterior angles- AEA corresponding angles - CA same side interior angles- SSI Types of angle pairs formed when a transversal cuts two parallel lines. vertical angles- VA linear pair of angles- LP same side exterior angles- SSE

13. s t c d 1 2 34 5 6 78 9 10 11 12 13 14 1516 s || t and c || d. Name all the angles that are congruent to  1. Give a reason for each answer.  3   1 corresponding angles  6   1 vertical angles  8   1 alternate exterior angles  9   1 corresponding angles  1   4 same side exterior angles  14   1 alternate exterior angles  5   10 alternate interior angles Parallel Lines and Transversals

14. Let’s Practice m<1=120° Find all the remaining angle measures. 1 4 2 6 5 78 3 60° 120° Parallel Lines and Transversals

15. Another practice problem Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements. 40° 120° 60° 40° 60° 180-(40+60)= 80° 80° 100° Parallel Lines and Transversals

16. Lesson 2-4: Angles and Parallel Lines16 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