1. Using Properties of Parallel Lines
Chapter 3 Section 3.5
Using Properties of Parallel Lines

2. Warm-Up
2x x – 9 = 180
5x – 5 = 180
5x = 185
x = 37

3. New Theorems
Theorem 3.11: If two lines are parallel to the same line then the lines are parallel to each other p q r
If p // r and r // q, then p // q

4. New Theorems
Theorem 3.12: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other m n p
If m  p and n  p, then m // n

5. State the postulate or theorem that allows you to conclude a // b
Two lines  to the same line then they are ||

6. State the postulate or theorem that allows you to conclude a // b
Corresponding Angle Postulate.

7. State the postulate or theorem that allows you to conclude a // b
If two lines are || to the same line, then they are || to each other.

8. Explain how you would show that a // b
Explain how you would show that a // b. State any postulates or theorems you would use.
If two lines  to the same line then they are ||
Alternate Exterior angle Converse

9. Explain how you would show that a // b
Explain how you would show that a // b. State any postulates or theorems you would use.
a || c – Alt. Int.  Converse
b || c – Cons. Int.  Converse
a || c – Two lines // to the same line are // to each other

10. Constructions We will come back to these at a later date
Construct a perpendicular thru a given point
Copy an angle
Construct a parallel thru a given point

11. Complete the Two Column Proof of Theorem 3.12
Given
Def.  Lines
Def.  Lines
Rt   thm.
Corres  Converse