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

Holt Geometry 3-1 Lines and Angles 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

Holt Geometry 3-1 Lines and Angles Identify parallel, perpendicular, and skew lines. Identify the angles formed by two lines and a transversal. Objectives

Holt Geometry 3-1 Lines and Angles Parallel Lines Def: line that do not intersect. Illustration: Notation: l || m AB || CD l m A B C D

Holt Geometry 3-1 Lines and Angles Examples of Parallel Lines Hardwood Floor Opposite sides of windows, desks, etc. Parking slots in parking lot Parallel Parking Streets: Franklin Ave & Bloomfield Ave

Holt Geometry 3-1 Lines and Angles Perpendicular Lines Def: Lines that intersect to form a right angle. Illustration: Notation: m  n Key Fact: 4 right angles are formed. m n

Holt Geometry 3-1 Lines and Angles Example of Perpendicular Lines Window panes Streets: Franklin Ave and Center Street

Holt Geometry 3-1 Lines and Angles Skew Lines Def: (NOT coplanar) Skew lines are NOT parallel lines and do not intersect Illustration: Notation: AE and CD are skew.

Holt Geometry 3-1 Lines and Angles Skew lines continued Are the following lines skew… 1. AE and FB? 2. FB and CG? 3. GH and CD? No, they are || Yes

Holt Geometry 3-1 Lines and Angles Parallel Planes are planes that do not intersect. Plane AEB || plane CGH

Holt Geometry 3-1 Lines and Angles Segments or rays are parallel, perpendicular, or skew if the lines that contain them are parallel, perpendicular, or skew. Helpful Hint

Holt Geometry 3-1 Lines and Angles Example 1: Identifying Types of Lines and Planes Identify each of the following. A. a pair of parallel segments B. a pair of skew segments C. a pair of perpendicular segments D. a pair of parallel planes LM ||QR KN and PQ NS  SP plane NMR || plane KLQ

Holt Geometry 3-1 Lines and Angles Check It Out! Example 1 Identify each of the following. a. a pair of parallel segments b. a pair of skew segments d. a pair of parallel planes c. a pair of perpendicular segments BF || EJ BF and DE are skew. BF  FJ plane FJH || plane BCD

Holt Geometry 3-1 Lines and Angles

Holt Geometry 3-1 Lines and Angles Example 2: Classifying Pairs of Angles Give an example of each angle pair. A. corresponding angles B. alternate interior angles C. alternate exterior angles 1 and 5 D. same-side interior angles 3 and 5 1 and 7 3 and 6

Holt Geometry 3-1 Lines and Angles Check It Out! Example 2 Give an example of each angle pair. A. corresponding angles B. alternate interior angles C. alternate exterior angles 1 and 3 D. same-side interior angles 2 and 7 1 and 8 2 and 3

Holt Geometry 3-1 Lines and Angles To determine which line is the transversal for a given angle pair, locate the line that connects the vertices. Helpful Hint

Holt Geometry 3-1 Lines and Angles Example 3: Identifying Angle Pairs and Transversals Identify the transversal and classify each angle pair. A. 1 and 3 B. 2 and 6 C. 4 and 6 transversal l corr. s transversal n alt. int s transversal m alt. ext s

Holt Geometry 3-1 Lines and Angles Check It Out! Example 3 Identify the transversal and classify the angle pair 2 and 5 in the diagram. transversal n same-side int. s.

Holt Geometry 3-1 Lines and Angles Lesson Quiz: Part I Identify each of the following. 1. a pair of parallel segments 2. a pair of skew segments 3. a pair of perpendicular segments 4. a pair of parallel planes EH || FG BF and EH CG  GH ABC and EFG

Holt Geometry 3-1 Lines and Angles Lesson Quiz: Part II Identify each of the following. 5. one pair alternate interior angles 6. One pair corresponding angles 7. one pair alternate exterior angles EHG and HGK 8. one pair same-side interior angles EHG and FGJ IHE and JGK EHG and HGF