1. Parallel Lines and Transversals
MCC8.G5. Students will understand and apply the properties of parallel and perpendicular lines and understand the meaning of congruence. a. Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically. b. Apply properties of angle pairs formed by parallel lines cut by a transversal. c. Understand the properties of the ratio of segments of parallel lines cut by one or more transversals.
Parallel Lines and Transversals

2. Lesson Essential Question:
What results can you find when a transversal intersects parallel lines?

4. Definition Two lines are parallel if they do not intersect. p q
p and q are not parallel m n

5. Parallel What would you call two lines which do not intersect?
A solid arrow placed on two lines of a diagram indicate the lines are parallel.
The symbol || is used to indicate parallel lines.
AB || CD

6. Transversal
Definition: A line that intersects two or more lines at different points.
When a transversal t intersects line n and m, angles of the following types are formed:
Exterior angles
Interior angles
Alternative exterior angles
Corresponding angles
Vertical angles t m n

7. We will be most concerned with transversals that cut parallel lines.
When a transversal cuts parallel lines, special pairs of angles are formed that are sometimes congruent and sometimes supplementary.

8. 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
Vertical angles
Continued…..

9. Vertical Angles & Linear Pair
Supplementary Angles:
Two angles that are opposite angles. Vertical angles are congruent.
 1   4,  2   3,  5   8,  6   7
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

10. Corresponding Angles & Consecutive Angles
Corresponding Angles: Two angles that are the same but in a different location.
 2   6,  1   5,  3   7,  4   8 1 2 3 4 5 6 7 8

11. 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

12. TRY IT OUT 2 1 3 4 6 5 7 8 60 degrees The m < 1 is 60 degrees.
What is the m<3 ?
60 degrees

13. TRY IT OUT
120 60 60
120
120 60 60
120

14. 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°

15. TRY IT OUT 2x + 20 x + 10 What do you know about the angles?
Write the equation.
Solve for x.
SUPPLEMENTARY
2x x + 10 = 180
3x + 30 = 180
3x = 150
x = 50

16. TRY IT OUT 3x - 120 2x - 60 What do you know about the angles?
Write the equation.
Solve for x.
ALTERNATE INTERIOR
3x = 2x - 60
x =
Subtract 2x from both sides
Add 120 to both sides