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

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

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

Lines & Planes (modeling) 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 Lines & Planes (modeling)

Parallel and Skew Parallel lines - 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 Parallel & Skew

Model the following situations in the items on your desk 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. Modeling situations

EX 1: ID Parallel & Skew Relationships 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 EX 1: ID Parallel & Skew Relationships

EX 1: ID Parallel & Skew Relationships 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 EX 1: ID Parallel & Skew Relationships

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

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

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

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

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

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

Corresponding Angles <1 & <5 ; <2 & <6 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 2 4 3 q <1 & <5 ; <2 & <6 <3 & <7 ; <4 & 8 r 6 5 7 8 Corresponding Angles

Ex 2: Classifying Angle Pairs 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 Ex 2: Classifying Angle Pairs

Ex 2: Classifying Angle Pairs 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 Ex 2: Classifying Angle Pairs

Ex 3: ID Transversal & Angle Pairs 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 Ex 3: ID Transversal & Angle Pairs

Ex 3: ID Transversal & Angle Pairs 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 Ex 3: ID Transversal & Angle Pairs