Project AMP
Dr. Antonio Quesada – Director, Project AMP
An Investigation of Parallel Lines and Associated Angles
By: Mike Berg, Kathy Miceli, and Rodney Rowell
Concept
The focus of this lesson is to explore the relationship that exists between angles and
parallel lines.
Project/Task
Each students of a high school geometry class will participate in activities that promote
understanding of parallel lines, transversals, and the angle pairs formed by those parallel
lines as found in the Ohio Proficiencies Outcomes. The students will use a geometry
software package such as Cabri Geometry or Geometer’s Sketchpad. The students will
then generalize the results to develop the theorems and postulates associated with
alternate interior, alternate exterior, and corresponding angle pairs.
Objectives
From the 12th grade Ohio Proficiency Outcomes:
#19 Students will demonstrate an understanding of angles of parallel and perpendicular
lines.
The learning objectives are:
Students will be able to determine measures of angles formed from parallel lines and
transversals.
Students will be able to make deductions from properties of angles formed from parallel
lines and transversals.
Learning Strategies
This activity is designed to be an introduction to a unit about parallel lines, so it is
assumed that the students know very little about parallel lines and associated angle pairs.
The students should be grouped in heterogeneous groups of two and should be supplied
with a student activity worksheet and a computer with a geometry software package, such
as Cabri Geometry or Geometer’s Sketchpad. Students may need instruction in using the
software. The students should work through the activity, discuss their results with
another group, and answer the questions at the end.
Assessment
The knowledge obtained about angles formed by parallel lines and a transversal will be
assessed by a quiz.
Tools and Resources
Student activity worksheet
Cabri Geometry or Geometer’s Sketchpad
Quiz
Protractor
Project AMP
Dr. Antonio Quesada – Director, Project AMP
An Investigation of Parallel Lines and Associated Angles
By: Mike Berg, Kathy Miceli, and Rodney Rowell
Do & How/Classroom and Information Management
Students should be placed in heterogeneous groups of two. Using the geometry software,
students should be instructed to draw to parallel lines and a transversal. The teacher may
want to review the definition of parallel lines. The students should then measure each of
the eight angles formed. The students should drag the transversal to different locations
and angles. The students should be asked to make conjectures about the measures of
alternate interior angles, alternate exterior angles, corresponding angles, interior angles
on the same side of the transversal, and exterior angles on the same side of the
transversal. After developing theses conjectures, the students should ask other groups
what they believe to be true about the aforementioned angle pairs. The students should
then proceed to answer questions that expand upon these relationships.
The teacher should act as a facilitator/moderator.
Results Sharing
After exploring the different angle pairs formed by a transversal intersecting two parallel
lines and discussing these relationships with another group, the students should
participate in a whole class discussion of the relationships and answered questions.
Dr. Antonio Quesada – Director, Project AMP
Project AMP
An Investigation of Parallel Lines and Associated Angles
By: Mike Berg, Kathy Miceli, and Rodney Rowell
Abstract
Subject:
Geometry
Grade Level:
High School
Strand:
Geometry
Students will analyze characteristics and properties of two- and three-dimensional
geometric shapes and develop mathematical arguments about geometric relationships.
Topic(s):
Parallel lines
Transversals
Alternate interior angles
Alternate exterior angles
Corresponding angles
Interior angles on the same side of the transversal
Exterior angles on the same side of the transversal
Objectives:
From the 12th grade Ohio Proficiency Outcomes:
#19 Students will demonstrate an understanding of angles of parallel and perpendicular
lines.
The learning objectives are:
Students will be able to determine measures of angles formed from parallel lines and
transversals.
Students will be able to make deductions from properties of angles formed from parallel
lines and transversals.
Materials:
Student activity worksheet
Cabri Geometry or Geometer’s Sketchpad
Quiz
Protractor
Expect Time:
2-3 40 minute class periods