Geometry: Unit 3 – Parallel and Perpendicular Lines
Unit Title: Parallel and Perpendicular Lines
Course: Geometry
Grade Levels: 10, 11, 12
Time Frame: 15 fifty minute class periods
Designer: Cheryl Maddox
Link to State Standards
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MA1 - addition, subtraction, multiplication and division; other number sense,
including numeration and estimation; and the application of these operations and
concepts in the workplace and other situations
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MA2 - geometric and spatial sense involving measurement (including length, area,
volume), trigonometry, and similarity and transformations of shapes
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MA4 - patterns and relationships within and among functions and algebraic,
geometric and trigonometric concepts
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MA5 - mathematical systems (including real numbers, whole numbers, integers,
fractions), geometry, and number theory (including primes, factors, multiples
Link to MAP Benchmarks
I.
II.
III.
IV.
V.
VI.
VIII.
Problem Solving
Communication
Reasoning
Connections
Number Sense
Geometric and Spatial Sense
Patterns and Relationships
Brief Summary of Unit
Students will study the angles formed when two lines are cut by a transversal. Students
will be introduced to several theorems and postulates related to parallel and perpendicular
lines.
What enduring understandings are desired?
Students will understand that:
 Pictures are a useful tool to help set up algebraic expressions.
 Parallel and perpendicular lines are a fundamental part of our world.
What essential questions will guide this unit and focus teaching?
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What are the relationships of the angles formed when two parallel lines are cut by a
transversal?
Can I find angle measures just by knowing certain properties?
How will I ever use these ideas?
What key knowledge and skills will students acquire as a result of this unit?
Students will know:
 Key terms: parallel lines, perpendicular lines, skew lines, parallel planes, transversal,
corresponding angles, alternate interior angles, alternate exterior angles, same-side
interior angles, converse
 The relationships between angles formed when two parallel lines are cut by a
transversal
 The angle relationships necessary to show two lines are parallel
Students will be able to:
 Determine whether lines are parallel, perpendicular or skew
 Use properties of angles to set up algebraic equations
 Identify corresponding angles, alternate interior and exterior angles, and same-side
interior angles
 Find missing angle measurement by applying theorems and postulates
 Show two lines are parallel by applying theorems and postulates
Performance Task After Unit 4
Other forms of assessment:
What will be assessed?
Mathematical understanding, reasoning, accuracy of work, and presentation of the
solution will be assessed.
How will evidence be collected?
 20 point quizzes: Homework quizzes will be given one per week to assess
understanding of homework
 50 point quizzes: To test student's understanding of smaller portions of the unit.
 Test: A test will be given at the end of the unit.
 Assignments: The students will be given an assignment after each lesson.
 Other: Each student will be expected to keep a geometry notebook consisting of
lesson notes, theorems, postulates, homework and corrections.
What type of assessment will be used?
 Selected response
 Academic prompt
 Questions and Answer
 Constructed Response
 Observation
 Work Sample
Description of the assessment
 75% from 20 point quizzes, 50 point quizzes and unit test
 25% from daily checks and homework scores
By what criteria will the student responses be evaluated?
 Homework will be graded in class each day by stating answers out loud. Students
will analyze their mistakes and make corrections.
 Homework quizzes will be graded on mathematical reasoning, accuracy and
presentation of work.
 Unit Test will be graded on mathematical reasoning, accuracy and presentation of
work.
 Notes, theorems and postulates will be checked periodically for completion and
accuracy.
Learning Experiences and Instruction
Where is the unit going?
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Post essential questions
Complete vocabulary terms to be used throughout the unit.
Hook the student
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Begin discussion on where in the classroom and in their homes do we see parallel and
perpendicular lines.
Discuss jobs that involve parallel and perpendicular lines (physical therapist, bicycle
designer, etc).
Discuss the "How will you use these ideas" section at the beginning of chapter 3
Parallel lines are not seen in all types of geometry.
Equip the student, explore the subject
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Explore the concepts of parallel and perpendicular lines and how they form angles
with certain relationships by learning how to draw a 3-dimensional box. Use the box
to discuss parallel, perpendicular and skew lines.
Equip the students with the knowledge of properties, theorems and postulates
involving parallel and perpendicular lines.
Discover relationships among pairs of angles when two lines are cut by a transversal.
Use notebook lines to form parallel lines and draw in a transversal. Use a protractor
to measure and make conjectures about pairs of angles.
Learn how to construct parallel and perpendicular lines using only a straight edge and
a compass.
Identify transformations using the graphing boards – specifically translations.
Rethink and revise opportunities
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After each lesson, there will be an assignment that reinforces the concepts
demonstrated in that lesson.
In addition to completing the current assignment, the students are expected to correct
the previous assignment hey evaluated that class period.
At the end of the unit, students will reflect upon the essential question by way of a
class discussion.
Evaluate performance and progress
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The students will maintain a geometry notebook consisting of lesson notes, examples,
theorems, postulates, assignments, corrections and vocabulary.
Students will participate in a review game of Jeopardy before the unit test.
Students will complete quizzes and a unit test over the material covered in unit 3.