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Two and Three Dimensional Shapes
Lesson 4
Lesson 4: “Ferb, I know what we’re going to do today!”
(Finding Angles Given Two Parallel Lines and a Transversal)
Introduction
This lesson introduces students to the concept of a transversal and teaches them how to find
the measure of various angles where the parallel lines and transversal intersect.
Instructional Outcomes
Students will be able to identify congruent angles formed by two parallel lines and a
transversal. Students will use appropriate mathematics vocabulary to identify pairs of angles.
Maine Learning Results:
Geometric Figures:
8.2: Students know and use angle properties of parallel lines to solve problems and determine
geometric relationships.
a. Know and use properties of angles created when parallel lines are cut by a transversal.
b. Use angle properties to determine whether lines are parallel.
Content Learning Outcome:
Know and explain angle relationships formed by parallel lines cut by a transversal.
Understand and verify congruence and similarity using physical models,
transparencies, or geometry software.
Common Core Standards:
Mathematics: Grade 8: Geometry: #5
Use informal arguments to establish facts about the angle sum and exterior angle of triangles,
about the angles created when parallel lines are cut by a transversal, and the angle-angle
criterion for similarity of triangles.
Assessment
Students will be able to demonstrate the ability to create two parallel lines intersected by a
transversal and given the measure of one angle, be able to identify all other associated angles
using the Triple-Entry Journal.
Literacy Support Strategies and Instruction
Before reading/learning:
Knowledge Rating Guide
Materials:
o Compass
o Protractor
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Ruler
The class will list out our “rules and guidelines” for how to use the necessary tools
for the lesson
During reading/learning:
Materials:
o Two-column notes
o Math journal
After reading/learning:
Knowledge Rating Guide using a second color to demonstrate differences
Materials:
o Journal entry
Homework Assignment:
Students will be able to demonstrate their understanding of parallel and transversal lines as
it applies to local community road maps. Maps of students’ communities are printed from
maps.google.com. Students will look for parallel-like roads and intersecting roads and make
mathematical observations and statements about the way the roads in the community are
laid out.
Before Reading/Learning
Literacy outcome:
Students will be able to state appropriate use for effective measuring and use of math tools
including protractors and the compass.
Teacher preparation:
1 inch wide strips of colored paper each at least 6 inches long. Each student will need two
brass brads to connect the “lines” of paper. Graph paper to lay the strips on and make sure
they are parallel.
Teacher facilitation:
We are going to create parallel lines with a transversal. Your brads will connect them. First lay
two strips of paper horizontally on your desk. Lay the third strip of paper so that it intersects
both of your parallel strips. The angle does not matter right now.
Now connect the intersecting strip to the parallel strips with a single brad. You will be able to
move the three connected strips when you are done. We will be able to change the angle
where the strips intersect because the brads allow us to rotate the papers.
Using your graph paper as a guide, I want you to experiment with your creation. What is the
largest angle you can create? What is the smallest?
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Now we are going to glue our lines to a piece of drawing paper to allow us to make some
permanent angles. Please do not create right angles, right angles work but won’t be as
effective as other angles for demonstrating the new ideas we are going to learn. (Check
student work before they glue down their work.)
Even though all of our papers may be slightly different, the rules of parallel lines with a
transversal will allow all of us to learn the same rules about geometry. I want you to use your
math tools to measure each of the angles you have created. What observations can you
make about those angles?
Look at your neighbors’ papers. What do you notice? What is true about all of our papers?
Let’s make a list. (Record observations on the board. Using the students’ observations, begin
giving the correct math language for students’ observations.)
The angles we are creating have descriptive names. Now that we know how angle
relationships work, let’s record the angle relationships on the sides of our papers. List the
following down the two sides and list the angles from your design that match these
descriptors.
Congruent angles
Vertical angles
Adjacent angles
Supplementary angles
Corresponding angles
Alternate interior angles
Alternate exterior angles
Let’s remember that MATH MAKES SENSE! Exterior means “outside” and interior
means “inside.”
During Reading/Learning
Literacy outcome:
Students will be able to explain how to find the measure of unknown angles given the
measure of a single angle, two parallel lines and a transversal
Teacher facilitation:
“We have a lot of vocabulary for this lesson. Which words do you already know? How is this
application of these words the same as you have used them before? How are they different?”
After Reading/Learning
Literacy outcome:
Students will be able to demonstrate their understanding of parallel and transversal lines
through a Quick Write activity.
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Teacher facilitation:
Given the maps of our communities, describe which roads are running parallel and which
roads act as transversals cutting through them. Use vocabulary related to the lines or angles
to describe your map.
Suggested Subsequent Lessons
Pythagorean theorem.
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