1. 3.1 Notes: Parallel Lines and Transversals
What does it mean when two lines are parallel, intersecting, or skew?

2. Vocab! Parallel Lines Coplanar lines that do not intersect Skew Lines
Parallel Lines
 Coplanar lines that do not intersect
Skew Lines
Lines that do not intersect and are not coplanar
Intersecting lines
 Lines that cross at a point

3. Example 1
Classify each of the following pairs of lines as parallel, intersecting, or skew.
Intersecting Lines
Parallel Lines
Intersecting Lines
Skew Lines
Skew Lines
Parallel Lines

4. You Try! 𝐹𝐺 , 𝐻𝐸 , 𝐷𝐴 𝐷𝐶 , one of many Plane DCF
a) Name all segments parallel to 𝐵𝐶 . b) Name a segment skew to 𝐸𝐻 . c) Name a plane parallel to plane ABG.
𝐹𝐺 , 𝐻𝐸 , 𝐷𝐴
𝐷𝐶 , one of many
Plane DCF

5. Vocab!
Transversal
 A line that intersects two or more coplanar lines at two different points.

6. Example 2 ∠2 & ∠4 ∠1 & ∠3 ∠6 & ∠8 ∠7 & ∠5 ∠1 & ∠2 ∠5 & ∠6
In the figure, two parallel lines are intersected by a third line called a transversal. a. Identify all the pairs of vertical angles. Explain your reasoning. b. Identify all the linear pairs of angles.
∠2 & ∠4 ∠1 & ∠3
∠6 & ∠8 ∠7 & ∠5
∠1 & ∠2 ∠5 & ∠6
∠4 & ∠3 ∠7 & ∠8

7. Lines in the two regions that are not between lines q and r
Interior Angles
 Exterior Angles   
Consecutive Interior Angles
Alternate Interior Angles
Alternate Exterior Angles
Corresponding Angles
Lines in the region
between lines q and r
∠3, ∠4, ∠5, ∠6
Lines in the two regions
that are not between
lines q and r
∠1, ∠2, ∠7, ∠8
Interior angles that lie
on the same side of
transversal t
∠4 & ∠5, ∠3 & ∠6
Nonadjacent interior angles
that lie on opposite sides of
transversal t
∠3 & ∠5, ∠4 & ∠6
Nonadjacent exterior angles
that lie on opposite sides of
transversal t
∠1 & ∠7, ∠2 & ∠8
Lie on the same side of
transversal t and on the same
side of lines q and r
∠1 & ∠5, ∠2 & ∠6, ∠3 & ∠7, ∠4 & ∠8

8. Example 3
Classify the relationship between the given angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. a) ∠2 and ∠ 6 b) ∠ 1 and ∠ 7 c) ∠ 3 and ∠ 8 d) ∠ 3 and ∠ 5
Corresponding angles: same side of transversal and same side of a & b
Alternate exterior: opposite sides of the transversal c
Consecutive interior angles: interior angles on the same side of c and the interior of a & b
Alternate interior: opposite sides of transversal t

9. You Try! Consecutive Interior Angles Corresponding Angles
Classify the relationship between the given angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. a) ∠4 and ∠ 5 b) ∠ 7 and ∠ 9 c) ∠ 4 and ∠ 7 d) ∠ 2 and ∠ 11
Consecutive Interior Angles
Corresponding Angles
Alternate Exterior Angles
Alternate Interior Angles

10. Example 5 Skip this slide
The driveways at a bus station are shown. Identify the transversal connecting the given angles. Then classify the relationship between the pair of angles. a) ∠1 and ∠ 2 b) ∠ 2 and ∠ 3 c) ∠ 4 and ∠ 5
Skip this slide

11. You Try! Consecutive interior angles Alternate exterior angles
1) 3 and 13 ____________________________________________________ Identify the transversal: 2) 8 and 10 ____________________________________________________ 3) 11 and 15 ___________________________________________________ 4) 8 and 6 _____________________________________________________ 5) 1 and 6 _____________________________________________________ 6) 6 and 10 ____________________________________________________ 7) 14 and 15 ___________________________________________________
Alternate exterior angles
Corresponding angles
Vertical angles
Alternate interior angles
Corresponding angles
Linear pair