Line and Angle Relationships

Line and Angle Relationships

? Carnegie Learning ? 2013 Carnegie Learning

The street plan of Washington, D.C., was designed by Pierre L'Enfant in the 1790s. Washington is laid out as a modified grid, with numbered streets running north-south, lettered streets running east-west, and avenues running diagonally.

5.1 Location, Location, Location! Line Relationships ......................................................223

5.2 When Lines Come Together

Angle Relationships Formed by

Two Intersecting Lines ................................................233

5.3 Crisscross Applesauce

Angle Relationships Formed by

Two Lines Intersected by a Transversal........................243

221

Models Worked Examples

Peer Analysis Talk the Talk Technology

Chapter 5 Overview

Thischapterfocusesonlineandanglecharacteristicsandrelationships.Itbeginswiththerelationshipsthatcan existbetweentwolines,thenmovestotherelationshipsbetweenangleswhenintersectedbyaline,andfinally concludeswithanglerelationshipsformedbytwolinescutbyatransversal.

Lesson

TEKS Pacing

Highlights

5.1

Line Relationships

8.8.D

Angle Relationships 5.2 FormedbyTwo 8.8.D Intersecting

Lines

Angle

Relationships

5.3

Formedby TwoLines

8.8.D

Intersectedbya

Transversal

Thislessondemonstratesthepossible

relationshipsthatcanexistbetween

1

twolines.

X

Questionsaskstudentstoidentify relationshipsgivendifferentmaps.

Thislessonreviewsthedifferent

1

anglerelationshipsthatexistbetween X X

X

intersectinglines.

Thislessoninvestigatesthe

relationshipsoftheanglemeasures

formedwhentwoparallelandtwonon-

parallellinesarecutbyatransversal.

1

X

Questionsaskstudentstosummarize theirconclusionsandsolveproblems forunknownanglemeasurements.

XX

? Carnegie Learning

221A ? Chapter 5 LineandAngleRelationships

Skills Practice Correlation for Chapter 5

Lesson

5.1

Line Relationships

Angle Relationships 5.2 FormedbyTwo Intersecting

Lines

Angle

Relationships

5.3

Formedby TwoLines

Intersectedbya

Transversal

Problem Set

1?6 7?12 13?18 19?24

1?6 7?12 13?18 19?24

1?6 7?12 13?16 17?22

Objectives

Vocabulary Describesketchesoflinerelationships Sketchexamplesoflinerelationships Describesketchesusinggivendescriptions Identifyexamplesoflinerelationshipsonamap Vocabulary Sketchexamplesofanglerelationships Identifyexamplesofanglerelationshipsonamap Completesketchesofanglerelationships Determineunknownanglemeasures Vocabulary Sketchexamplesofline-anglerelationships Identifyexamplesofline-anglerelationshipsonamap Completestatementsusing"congruent"or"supplementary" Determinemeasuresofangles

? Carnegie Learning

Chapter 5 LineandAngleRelationships ? 221B

? Carnegie Learning

222 ? Chapter 5 LineandAngleRelationships

Location, Location, Location!

Line Relationships

Learning Goal

In this lesson, you will:

Explorepossiblerelationships

betweentwolinesinEuclidean geometry.

Key Terms

intersectinglines plane perpendicularlines parallellines

coplanarlines skewlines coincidentallines

Essential Ideas

? Intersecting lines are lines that cross through

each other.

? Perpendicular lines are lines that intersect at a

right angle.

? Parallel lines are lines that lie in the same plane and

do not intersect.

? Coplanar lines are lines that lie in the same plane. ? Skew lines are lines that do not lie in the same plane. ? Coincidental lines are lines that have equivalent linear

equations and overlap at every point when they are graphed.

? If two lines are coplanar, then they intersect at a

single point, intersect at an infinite number of points, or do not intersect.

Texas Essential Knowledge and Skills for Mathematics

Grade 8 (8) Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to:

(D) use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles

Materials

Protractor Straightedge

? Carnegie Learning

5.1 LineRelationships ? 223A

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