1. Angles and Parallel Lines
MCC8.G.5
Angles and Parallel Lines

2. Intersecting Lines
Lines that cross at exactly one point.

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

4. PARALLEL LINES Def: line that do not intersect. Illustration:
Notation: l || m AB || CD A B C D l m

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

6. Examples of Parallel Lines
Streets: Belmont & School

7. Transversal
Definition: A line that intersects two or more lines in a plane at different points is called a transversal. t m n

8. Vertical Angles & Linear Pair
Two angles that are opposite angles. Vertical angles are congruent.
 1   4,  2   3,  5   8,  6   7
Supplementary angles that form a line (sum = 180)
1 & 2 , 2 & 4 , 4 &3, 3 & 1,
5 & 6, 6 & 8, 8 & 7, 7 & 5 1 2 3 4 5 6 7 8

9. Supplementary Angles/ Linear Pair
Two angles that form a line (sum=180) 1 2 3 4 5 6 7 8 t
1+2=180
2+4=180
4+3=180
3+1=180
5+6=180
6+8=180
8+7=180
7+5=180

10. Supplementary Angles/ Linear Pair
Find the measures of the missing angles t ?
108 
72  ?
108 

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

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

13. Angles and Parallel Lines
If two parallel lines are cut by a transversal, then the following pairs of angles are congruent.
Corresponding angles
Alternate interior angles
Alternate exterior angles
If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary.
Consecutive interior angles
Consecutive exterior angles
Continued…..

14. Corresponding Angles
Corresponding Angles: Two angles that occupy corresponding positions.
 2   6,  1   5,  3   7,  4   8 1 2 3 4 5 6 7 8

15. Consecutive Angles
Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal.
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 1 2
m1 +m7 = 180º, m2 +m8 = 180º 3 4 5 6 7 8

16. 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 1 2 3 4 5 6 7 8

17. 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. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A
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°

18. If line AB is parallel to line CD and s is parallel to t, find:
Example:
1. the value of x, if m<3 = 4x + 6 and the m<11 = 126.
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. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A
ANSWERS:
1. 30
2. 35
3. 33