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

Agenda 3-1 Notes Practice/Homework

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:

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

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

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:

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

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:

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

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”

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

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

Homework: Worksheet