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

Mathematical Practices Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. CCSS

Lines & Planes (modeling) LESSON 3-1: Parallel Lines & Transversals Lines & Planes Two lines intersect in a point A line intersects a plane at a point and a line Two planes intersect in a line Lines & Planes (modeling)

Parallel and Skew Parallel lines - Coplanar lines that DON’T intersect Parallel planes - Planes that DON’T intersect Plane A Plane B Skew lines - NOT Parallel DON’T Intersect NOT Coplanar Lines a and f are skew lines Parallel & Skew

A. Name a plane that is parallel to plane RST. A. plane WTZ B. plane SYZ C. plane WXY D. plane QRX Example 1a

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

Parallel Lines and Transversals Two lines divide the plane into three regions. The region between the lines is referred to as the interior. The two regions not between the lines is referred to as the exterior. Exterior Interior

b l m c t r Definition of Transversal In a plane, a line is a transversal iff it intersects two or more Lines, each at a different point. The lines cut by a transversal may or may not be parallel. l m 1 2 3 4 5 7 6 8 Parallel Lines t is a transversal for l and m. t 1 2 3 4 5 7 6 8 b c Nonparallel Lines r is a transversal for b and c. r

When a transversal intersects two lines, _____ angles are formed. eight These angles are given special names. l m 1 2 3 4 5 7 6 8 t Interior angles lie between the two lines. Exterior angles lie outside the two lines. Alternate Interior angles are on the opposite sides of the transversal. Alternate Exterior angles are on the opposite sides of the transversal. Consectutive Interior angles are on the same side of the transversal. ?

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

HOMEWORK Pgs. 175-178 #’s 1-12, 15, 21-30, 38-43, 51, 55-58