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

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

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

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

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

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

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

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

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

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

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