3-1 Lines and Angles Warm Up Lesson Presentation Lesson Quiz Holt Geometry Warm Up Lesson Presentation Lesson Quiz

Warm Up Identify each of the following. 1. points that lie in the same plane 2. two angles whose sum is 180° 3. the intersection of two distinct intersecting lines 4. a pair of adjacent angles whose non-common sides are opposite rays coplanar points supplementary angles point linear pair

Objectives Identify parallel, perpendicular, and skew lines. Identify the angles formed by two lines and a transversal.

Parallel Lines Def: lines that do not intersect. Illustration: Notation: l || m AB || CD A B C D l m

Examples of Parallel Lines Hardwood Floor Opposite sides of windows, desks, etc. Parking slots in parking lot Streets: Franklin Ave & Bloomfield Ave

Perpendicular Lines Def: Lines that intersect to form a right angle. Illustration: Notation: m  n Key Fact: 4 right angles are formed. m n

Example of Perpendicular Lines Streets: Franklin Ave and Center Street

Skew Lines Def: (NOT coplanar) Skew lines are NOT parallel lines and do not intersect Illustration: Notation: AE and CD are skew.

Skew lines continued Are the following lines skew…? Yes, they are skew 1. AE and FB? No, they are || 2. FB and CG? No, they are || -- even though we can’t see it, a plane COULD connect them 3. AE and BD? Yes, they are skew

are planes that do not intersect. Parallel Planes are planes that do not intersect. Plane AEB || plane CGH

Segments or rays are parallel, perpendicular, or skew if the lines that contain them are parallel, perpendicular, or skew. Helpful Hint

Check It Out! Example 1 Identify each of the following. a. a pair of parallel segments BF || EJ b. a pair of skew segments BF and DE are skew. c. a pair of perpendicular segments BF  FJ d. a pair of parallel planes plane FJH || plane BCD

Example 1: Identifying Types of Lines and Planes Identify each of the following. E. a pair of parallel segments LM ||QR F. a pair of skew segments KN and PQ G. a pair of perpendicular segments NS  SP H. a pair of parallel planes plane NMR || plane KLQ

Lesson Quiz: Part I Identify each of the following. I. a pair of parallel segments EH || FG J. a pair of skew segments BF and EH K. a pair of perpendicular segments CG  GH L. a pair of parallel planes ABC and EFG

Parallel neither perpedicular

No, they intersect Yes, they are skew.

Plane C Plane D

1. Line x and line y 2. Line x and line z 3. Line y and line z

4. QU TX ST RQ 5. Plane RST 6. WS WX UV RV