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Progressive Mathematics Initiative
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Mathematics Curriculum
Unit Plan # 3
Title: Parallel Lines
Subject: Geometry
Length of Time: 2.5 weeks
Unit Summary: In this unit, students will apply theorems involving parallel and perpendicular lines to solve
problems and construct proofs.
Learning Targets
PARCC
Major Clusters;
Supporting Clusters;
Additional Clusters
Conceptual Category: Function Domain: Congruence
Cluster: Experiment with transformations in the plane.
Standard#:
Standard:
Know precise definitions of angle, circle, perpendicular line, parallel line, and line
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segment, based on the undefined notions of point, line, distance along a line, and
distance around a circular arc.
Conceptual Category: Functions Domain: Congruence
Cluster: Prove geometric theorems.
Standard#:
Standard:
Prove theorems about lines and angles. Theorems include: vertical angles are
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congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent and corresponding angles are congruent; points on a perpendicular
bisector of a line segment are exactly those equidistant from the segment’s
endpoints.
Conceptual Category: Functions Domain: Congruence
Cluster: Make geometric constructions.
Standard#:
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Standard:
Make formal geometric constructions with a variety of tools and methods (compass
and straightedge, string, reflective devices, paper folding, dynamic geometric
software, etc.). Copying a segment; copying an angle; bisecting a segment;
bisecting an angle; constructing perpendicular lines, including the perpendicular
bisector of a line segment; and constructing a line parallel to a given line through a
point not on the line.
Domain: Standards for Math Practice
Standard#:
Standard:
MP1
Making sense of problems and persevere in solving them.
MP2
Reason abstractly and quantitatively.
MP3
Construct viable arguments and critique the reasoning of others.
MP4
Model with mathematics.
MP5
Use appropriate tools strategically.
MP6
Attend to precision.
MP7
Look for and make use of structure.
MP8
Look for and express regularity in repeated reasoning.
Unit Essential Questions:
Unit Enduring Understandings:
 Can I logically communicate my
 Not all lines and not all planes intersect.
mathematical reasoning in writing as well as
 When a line intersects two or more lines, the angles
orally?
formed at the intersection points create special
angle pairs.
 How do you prove that two lines are
 The special angle pairs formed by parallel lines and
parallel?
Geometry – Parallel Lines
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

a transversal are either congruent or supplementary.
Certain angle pairs can be used to decide whether
two lines are parallel/perpendicular.
Use basic construction techniques to explore
properties.
Unit Objectives:
 Students will be able to identify pairs of angles formed by two lines cut by a transversal.
 Students will be able to apply the properties of angles formed by parallel lines and a transversal.
 Students will be able to use information about angles to conclude whether or not lines are
parallel/perpendicular.
 Students will be able to identify corresponding, alternate-interior, alternate-exterior, and same-side
interior angles and then find the missing angles or solve for x.
 Students will be able to construct parallel lines.
Evidence of Learning
Formative Assessments:
 SMART Response questions used throughout the unit.
 3 Quizzes
Summative Assessment:
 Unit Test
Lesson Plans
Topics
Timeframe
Topic 1: Lines: Intersecting, Parallel & Skew
1
Topic 2: Lines & Transversals
1
Quiz 1
0.5
Lab: Starting a Business
1
Topic 3: Parallel Lines & Proofs
2
Quiz 2
0.5
Topic 4: Properties of Parallel Lines
Lab: Properties of Parallel Lines
Quiz 3
3
0.5
Topic 5: Constructing Parallel Lines
1
Review and Unit Test
2
Curriculum Resources:
 www.njctl.org/courses/math/geometry/
 http://www.mathsisfun.com/geometry/construct-paranotline.html
 Lab 1: Properties of Parallel Lines
Lesson Components
21st Century Skills
 Financial, Economic, Business, and Entrepreneurial Literacy
21st Century Themes
 Critical Thinking and Problem Solving
 Communication and Collaboration
 Life and Career Skills
Geometry – Parallel Lines
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