2. MCC8.G.5 Angles and Parallel Lines

3. Intersecting Lines Lines that cross at exactly one point. Think of an intersection, where two roads cross each other.

4. Perpendicular Lines Lines that intersect to form right angles.

5. PARALLEL LINES Definition: lines that do not intersect. Think: railroad tracks! Here’s how it looks: This is how you write it: l | | m A B | | CD This is how you say it: “Line l is parallel to line m” and “Line AB is parallel to line CD” l m A B C D

6. Examples of Parallel Lines Hardwood Floor Opposite sides of windows, desks, etc. Parking slots in parking lot Parallel Parking Streets

7. Examples of Parallel Lines Streets: Belmont & School

8. Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal. Line t is a transversal here, because it intersects line m and line n. t m n

9. Vertical Angles & Linear Pair Vertical Angles: Linear Pair:  1   4,  2   3,  5   8,  6   7 (The symbol  means congruent, in case you’ve forgotten) Two angles that are opposite angles. Vertical angles are congruent, which means they’re equal. These are linear pairs:  1 &  2,  2 &  4,  4 &  3,  3 &  1,  5 &  6,  6 &  8,  8 &  7,  7 &  5 Supplementary angles that form a line (sum = 180  ) 12 34 56 78

10. Linear Pairs Two (supplementary and adjacent) angles that form a line (sum=180  ) 12 3 4 5 6 78 t  5+  6=180  6+  8=180  8+  7=180  7+  5=180  1+  2=180  2+  4=180  4+  3=180  3+  1=180

11. Can you… Find the measures of the missing angles? ? 72  ? t 108  180 - 72

12. Complementary Angles Two angles whose measures add to 90˚.

13. Adjacent Angles Angles in the same plane that have a common vertex and a common side.

14. 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 Continued…..

15. Corresponding Angles Corresponding Angles: Two angles that occupy corresponding positions.  2   6,  1   5,  3   7,  4   8 12 34 56 78

16. Consecutive Angles Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. (Think “interior” as in, inside the parallel lines…) Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m  3 +m  5 = 180º, m  4 +m  6 = 180º m  1 +m  7 = 180º, m  2 +m  8 = 180º 12 34 56 78

17. Alternate Angles Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal.  3   6,  4   5  2   7,  1   8 12 34 56 78

18. 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 Hint: First, find angle 2! Use the measure of angle 1 to get your started.

19. 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