Lesson 3 1 Parallel Lines Transversals TARGETS Identify

Lesson 3 -1: Parallel Lines & Transversals TARGETS • Identify relationships between two lines or two planes. • Name angle pairs formed by parallel lines and transversals

Content Standards G-CO. 1 Experiment with transformations in the plane. Mathematical Practices 2 Reason abstractly and quantitatively. 6 Attend to precision.

• Parallel line • Alternate interior angles • Skew lines • Alternate exterior angles • Parallel planes • Corresponding anlges • Transversal • Interior angles • Exterior angles • Consecutive interior angles

LESSON 3 -1: Parallel Lines & Transversals Lines & Planes Model the following situations in the items on your desk Two lines intersect in a point A line intersects a plane at a point Two planes intersect in a line

LESSON 3 -1: Parallel Lines & Transversals Parallel and Skew Parallel lines - Coplanar lines that DO NOT intersect Parallel planes - Planes that DO NOT intersect Plane A Plane B Skew lines - Lines that DO NOT intersect and are not coplanar Lines l and m are skew lines

LESSON 3 -1: Parallel Lines & Transversals Lines & Planes Model the following situations in the items on your desk 1) Two lines are parallel. 2) Two planes are parallel 3) Two lines are skew 4) Two lines are parallel. Both lines intersect a plane in 2 distinct points. 5) Two lines intersect a plane in two distinct points. The two lines are skew.

LESSON 3 -1: Parallel Lines & Transversals EXAMPLE 1 Identify Parallel and Skew Relationships A. Name all segments parallel to BC. AD, EH, FG B. Name a segment skew to EH. AB, CD, BG, or CF C. Name a plane parallel to plane ABG. plane CDE

LESSON 3 -1: Parallel Lines & Transversals EXAMPLE 1 Identify Parallel and Skew Relationships A. Name a plane that is parallel to plane RST. plane WXY B. Name a segment that intersects YZ. WZ, XY, TS, or SY C. Name a segment that is parallel to RX. QW, TZ, or SY

LESSON 3 -1: Parallel Lines & Transversals d Transversal A line that intersects two or more coplanar lines at two different points line d 1 4 2 3 q 5 6 8 7 r

LESSON 3 -1: Parallel Lines & Transversals d Interior Angles Lie in the region between lines q and r 1 4 2 3 q <3, <4, <5, <6 5 6 8 7 r

LESSON 3 -1: Parallel Lines & Transversals d Exterior Angles Lie in the two regions not between lines q and r 1 4 2 3 q <1, <2, <3, <4 5 6 8 7 r

LESSON 3 -1: Parallel Lines & Transversals d Consecutive Interior Angles 1 4 A pair of interior angles that lie on the same side of the transversal (d ) <4 & <5 <3 & <6 2 3 q 5 6 8 7 r

LESSON 3 -1: Parallel Lines & Transversals d Alternate Interior Angles Nonadjacent interior angles that lie on opposite sides of the transversal (d ) <3 & <5 <4 & <6 1 4 2 3 q 5 6 8 7 r

LESSON 3 -1: Parallel Lines & Transversals d Alternate Exterior Angles Nonadjacent exterior angles that lie on opposite sides of the transversal (d ) <1 & <7 <2 & <8 1 4 2 3 q 5 6 8 7 r

LESSON 3 -1: Parallel Lines & Transversals d Corresponding Angles Lie on the same side of transversal ( d ) and on the same side of lines q and r <1 & <5 ; <2 & <6 <3 & <7 ; <4 & 8 1 4 2 3 q 5 6 8 7 r

LESSON 3 -1: Parallel Lines & Transversals EXAMPLE 2 Classify Angle Pair Relationships Classify the relationship between the following angle pairs alternate interior, alternate exterior, corresponding, or consecutive interior angles. A. 2 and 6 corresponding B. 1 and 7 alternate exterior C. 3 and 8 consecutive interior D. 3 and 5 alternate interior

LESSON 3 -1: Parallel Lines & Transversals EXAMPLE 2 Classify Angle Pair Relationships Classify the following relationships: A. 4 and 5. consecutive interior B. 7 and 9. corresponding C. 4 and 7. alternate exterior D. 2 and 11. alternate interior

LESSON 3 -1: Parallel Lines & Transversals EXAMPLE 3 Identify Transversals and Classify Angle Pairs BUS STATION The driveways at a bus station are shown. Identify the transversal connecting the angles and then classify the relationship between the pair of angles. A. 1 and 2 line v; corresponding angles B. 2 and 3 line v; alternate interior angles C. 4 and 5 line y; consecutive interior angles

LESSON 3 -1: Parallel Lines & Transversals EXAMPLE 3 Identify Transversals and Classify Angle Pairs HIKING A group of nature trails is shown. Identify the sets of lines to which the given line is a transversal: A. line a lines c, d, e, f B. line b lines c, d, e, f C. line c lines a, b, d, e, f