1. 3-1 Properties of parallel Lines
Unit 3 Day 1
3-1 Properties of parallel Lines

2. Agenda
3-1 Notes
Practice/Homework

3. Warm-Up Describe the vector that represents the algebraic rule:
Write the algebraic rule for the translation 4 to the right and 3 down.
Write the two statements that make up the biconditional:

4. Parallel Lines Equations of ll lines have the same slope
They never touch
Ex:

5. Line t is a transversal through Line l and line m
Transversal: Is a line that intersects two coplanar lines at two distinct points.
Line t is a transversal through Line l and line m

6. Alternate interior angles
On the inside of the two ll lines and on opposite sides of the transversal.
Make a “Z”
<3 and <6 are Alt. Int. Ang. Other sets of alternate interior angles:

7. Alternate Interior Angles Theorem:
If a transversal intersects two parallel lines, then alternate interior angles are congruent
<3 ≅ <6
<5 ≅ <4

8. Same-Side interior angles
On the inside of the two parallel lines and on the same side of the transversal.
Makes a “C”
<4 and <6 are S.S. Int Ang. Other sets of S.S. int angles:

9. 3. Same-Side Interior Angles Theorem
If a transversal intersects two parallel lines, then same-side interior angles are supplementary
m<4+m<6 = 180
m<3 + m<5 = 180

10. Corresponding Angle
<4 and <8 are corr. < Other sets of Corr. <:
Treat each ll line as a separate: Corresponding angles are in the same “position”
Makes a “F”

11. 1. Corresponding Angles Postulate:
If a transversal intersects two parallel lines, then corresponding angles are congruent.
<1 ≅ <5
<3 ≅ <7
<2 ≅ <6
<4 ≅ <8

12. Find the measure of each missing angle, which theorem/Postulate Justifies:

15. Homework:
Worksheet