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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