Progressive Mathematics Initiative
www.njctl.org
Mathematics Curriculum
Unit Plan # 2
Title: Parallel Lines
Subject: Geometry
Length of Time: 3 weeks
Unit Summary: In this unit, students will apply theorems involving parallel and perpendicular lines to solve
problems and construct proofs.
Learning Targets
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#:
G.CO.12
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.
Unit Essential Questions:
 Can I logically communicate my
mathematical reasoning in writing as well as
orally?
 How do you prove that two lines are
parallel?
Unit Enduring Understandings:
 Not all lines and not all planes intersect.
 When a line intersects two or more lines, the angles
formed at the intersection points create special
angle pairs.
 The special angle pairs formed by parallel lines and
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
1.5
Topic 2: Lines & Transversals
1.5
Quiz 1
0.5
Topic 3: Parallel Lines & Proofs
2
Lab: Starting a Business
1
Quiz 2
0.5
Topic 4: Properties of Parallel Lines
Lab: Properties of Parallel Lines
Quiz 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
3