Download Alternate Exterior Angles

Help me Find my Relationship!
Resource ID#: 38211
Primary Type: Lesson Plan
This document was generated on CPALMS - www.cpalms.org
In this lesson, students will investigate the relationship between angles when parallel lines are
cut by a transversal. Students will identify angles, find angle measures, and they will use the free
application GeoGebra (see download link under Suggested Technology) to provide students with
a visual representation of angles relationships.
Subject(s): Mathematics
Grade Level(s): 8
Intended Audience: Educators
Suggested Technology: Computer for Presenter, Internet Connection, LCD Projector, Java
Plugin, GeoGebra Free Software (Download the Free GeoGebra Software)
Instructional Time: 2 Hour(s)
Freely Available: Yes
Keywords: Transversal, interior angles, exterior angles, corresponding angles, alternate interior
angles, alternate exterior angles
Instructional Component Type(s): Lesson Plan
Instructional Design Framework(s): Direct Instruction
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Activity2 revisions.doc
Activity1 revisions.doc
LESSON CONTENT

Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this
lesson?
Using GeoGebra and one other method (graph paper, colored pencils and patty paper), student will describe
the relationship between angles on parallel lines cut by a transversal; identify another pair of angles with
the same relationship; and achieve 100% on the independent practice.

Prior Knowledge: What prior knowledge should students have for this lesson?
Students must have prior knowledge and understanding of angles in a polygon, identifying congruent
figures, similarity and solving two-step equations. In addition, they must know how to use a ruler and
protractor to measure angles. It would be helpful if the students had some prior experience manipulating
constructions using GeoGebra. (GeoGebra is a free software application that can be accessed at
http://www.geogebra.org/cms/)

Guiding Questions: What are the guiding questions for this lesson?
1.
2.
3.
4.
5.
6.
7.
8.
9.

What is a transversal? ("a line that intersects two or more lines at different points.")
If we have two parallel lines or non-parallel lines cut by a transversal, how many angles are
created? ("8")
What are exterior angles? ("angles that lie on the outside of the parallel lines cut by the
transversal.")
What are interior angles? ("angles that lie between the parallel lines cut by the transversal.")
What are vertical angles? (" a pair of angles opposite to each other formed by two intersecting
lines.")
What are alternate interior angles? ("pair of angles between the parallel lines and on opposite
sides of the transversal.")
What are alternate exterior angles?("pair of angles on the outside of the parallel lines and on
opposite sides of the transversal.")
What is the difference between alternate interior angles and alternate exterior angles? (Alternate
interior angles are between the parallel lines and on opposite sides of the transversal while
alternate exterior angles are outside the parallel lines and on opposite sides of the transversal.)
What are corresponding angles? ("If two angles occupy corresponding positions, they are called
corresponding angles. If the lines intersected by the transversal are parallel, the corresponding
angles are congruent.")
Teaching Phase: How will the teacher present the concept or skill to students?
During the Teaching Phase, teacher uses the GeoGebraTube applet "Parallel Lines Cut by a Transversal" to
give visual definitions and demonstrations of angle relationships.
Transversal
Definition
"A Transversal is a line that intersects two or more different lines at different points."
Demonstration
o
o
o
o
o
Clear all boxes in the GeoGebraTube applet
Check the box next to "Show all angles" to show the 8 angles that are formed.(Guiding Question
#2)
Move points A or B to change the orientation of the parallel lines.
Move points C or D to change the orientation of the transversal.
Ask: "What happens when the orientations of the transversal or parallel lines change?" (There are
always 8 angles.)
Transversal Examples
Teacher then asks students to look around the classroom. Have students identify and call out examples of
two lines with an intersecting transversal. Examples might be:
o
o
o
o
Tile patterns in the ceiling
Filing cabinet drawers
Windows
Letter "Z"
(See examples in the photographs below)
Related Terminology
After discussing classroom examples of transversals and parallel lines, the teacher proceeds with
definitions and demonstrations of important terms. The terms include:
o
o
o
o
o
o
Vertical Angles
Interior Angles
Exterior Angles
Alternate Interior Angles
Alternate Exterior Angles
Corresponding Angles
Vertical Angles
Definition
"Interior Angles are the angles that lie between two parallel lines cut by a transversal." (Guiding Question
#4)
Demonstration
o
o
Clear all checkboxes in the GeoGebraTube applet.
Using GeoGebra, check the box "Interior Angles." This gives students a visual representation of
interior angles.
Exterior Angles
Defintion
"Exterior Angles are the angles that lie on the outside of two parallel lines cut by a transversal." (See
Guiding Question #3)
Demonstration
o
o
Clear all checkboxes in the GeoGebraTube applet.
Check the box "Exterior Angles." This gives students a visual representation of interior angles.
Alternate Interior Angles
Teacher Note - During demonstration of alternate interior angles, the teacher can optionally introduce
complementary and supplementary angles.
Definition
"Alternate Interior Angles are the pair of angles between the parallel lines and on opposite sides of a
transversal." (Guiding Question #6)
Demonstration
o
o
o
o
Clear all checkboxes in the GeoGebraTube applet.
Check the box "Alternate Interior" angles to give students a visual representation of alternate
interior angles.
Move points A & B as well as C & D to change the orientations of the two parallel lines and the
transversal. Ask students what they notice. ("Alternate interior angles are always equal.")
Check the box "Interior Angles." Ask students to identify the other pair of alternate interior angles.
Alternate Exterior Angles
Teacher Note - During demonstration of alternate exterior angles, the teacher can optionally introduce
complementary and supplementary angles.
Definition
"Alternate Exterior Angles are the pair of angles on the outside of the parallel lines and on opposite sides of
a transversal." (Guiding Question #7)
Demonstration
o
o
o
o
o
Clear all checkboxes in the GeoGebraTube applet.
Check the box "Alternate Exterior" angles. This gives students a visual representation of alternate
exterior angles.
Move points A & B as well as C & D to change the orientations of the two parallel lines and the
transversal.
Ask students what they notice. ("Alternate exterior angles are always equal.")
Check the box "Exterior Angles." Ask students to identify the other pair of alternate exterior
angles.
Corresponding Angles
Definition
"Two angles that occupy corresponding positions are called Corresponding Angles." (Guiding Question #9)
Demonstration
o
Clear all checkboxes in the GeoGebraTube applet.
o
o
o

Check the box "Corresponding Angles." This gives students a visual representation of
corresponding angles.
Use GeoGebra to highlight other pairs of corresponding angles. Teacher may check boxes 2, 3 and
4 (one at a time) to show them.
Using GeoGebra to demonstrate, ask students to conjecture the relationship between
corresponding angles, for any orientation of the two parallel lines and transversal. ("The measures
of corresponding angles are always equal; in other words, they are congruent.")
Guided Practice: What activities or exercises will the students complete with teacher
guidance?
Activity 1
Students will use patty paper and pencil to discover vertical angles when a transversal cuts two parallel
lines.
Students Practice
o
o
o
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Give each student a sheet of patty paper and the Activity-1.doc worksheet.
While students work, teacher circulates to help students and clarify misconceptions.
When students are finished, refocus them as a whole for the discussion.
Have students share which pairs of vertical angles they found. (“Angles 1 & 4; Angles 2 & 3;
Angles 5 & 8; Angles 6 & 7”)
Students share what these vertical angles have in common. ("They are opposite from each other;
they have the same measure; their angles are congruent".)
Activity 1 Answers
5.
6.
7.
8.
9.
10.
11.
12.
Congruent pair of angles: 1 & 4, 1 & 5 and 1 & 8.
Angle 4.
Vertical Angles.
Congruent pair of angles: 2 & 3, 2 & 6 and 2 & 7.
Angle 6 and Angle 7.
Angles 6 and 7 are congruent vertical angles.
Vertical angles are the pair of angles opposite to each other formed by two intersecting lines.
Vertical Angles: 1 & 4, 2 & 3, 5 & 8, 6 & 7.
Common Mistakes
o
o
Not realizing vertical angles are always equal.
Not finding vertical angles correctly.
Activity 2
Students will use patty paper and colored pencil to discover alternate interior and alternate exterior angles
when a transversal cuts two parallel lines.
Students Practice
o
o
Students do the Activity-2 worksheet.
While students work, teacher circulates to help students and clarify misconceptions.
o
o
When students are finished, refocus them as a whole for the discussion.
Students share their answers for the activity.
Activity 2 Answers
19.
20.
21.
22.
23.
24.
Angle 6
Angle 5
Alternate interior angles
Angle 8
Angle 7
Alternate exterior angle
Common Mistakes
o
o
Mixing up interior and exterior angles.
Not realizing that alternate interior and alternate exterior angles must be on the opposite side of the
transversal.
Activity 3
Students will use patty paper and colored pencil to discover corresponding angles when a transversal cuts
two parallel lines.
Students Practice
o
o
o
o
Students do the Activity-3 worksheet.
While students work, teacher circulates to help students and clarify misconceptions.
When students are finished, refocus them as a whole for the discussion.
Students share their answers for the activity.
Activity 3 Answers
31.
32.
33.
34.
35.
36.
Angle 5
Angle 7
Angle 6
Angle 8
Corresponding Angles
Corresponding Angles: 1 & 5, 3 & 7, 2 & 6, 4 & 8
Common Mistakes
o
o

Not finding corresponding angles correctly
Not seeing that corresponding angles are located on the same position on parallel lines.
Independent Practice: What activities or exercises will students complete to reinforce
the concepts and skills developed in the lesson?
Students will be given Homework that will be handed in the following day for assessment. The homework
is designed to reinforce the day's class work. If students struggle on the homework, the teacher will be
made aware of misunderstandings, and shortcomings of the lesson taught. When "weak" areas are identified
on the homework, the teacher can address the areas during the next available class period.

Closure: How will the teacher assist students in organizing the knowledge gained in the
lesson?
Summarize lesson by asking students to debrief on what they learned on this lesson. Have students to share
what they discovered about the angles by knowing certain information about the angles formed by a
transversal. The teacher will be sure to focus on reinforcing the vocabulary with the class and will ask
students to explain what they learned as a result of the lesson.

Summative Assessment
The teacher will use the homework assignment to determine if the students have reached the learning
targets for this lesson. Students must show 100% mastery in the homework assignment in order for the skill
to be considered mastered.

Formative Assessment
Teacher will give students a quiz to gather information about student understanding.

Feedback to Students
Teacher will gives feedback to students during Activities 1, 2, and 3 of the guided practice. The student
feedback includes discussion of possible misconceptions.
ACCOMMODATIONS & RECOMMENDATIONS

Accommodations:
During this lesson students are working on real-world problem to contextualize the concepts, this will help
visual learners to comprehend better the concept. Students will be working on hands on activities, which
will reinforce the skill. Students will be also working in pairs to brainstorm and complete different tasks
during the each activity, this think-share-pair strategy will allow students to learn from each other. Teacher
will circulate continuously, monitor and check in with each group on their progress and understanding of
the tasks.

Extensions:
The lesson itself can stand alone or can be extended to master other related skills. Teacher might like to
extend angles relationships and introduce complementary and supplementary angles. Students can apply
one or two step equations to find missing angle based on the definition of complementary and
supplementary angles. Teacher might also have students to create a map of the streets where they live and
have students to identify corresponding, vertical, alternate exterior or alternate interior angles.

Suggested Technology: Computer for Presenter, Internet Connection, LCD Projector, Java Plugin,
GeoGebra Free Software

Special Materials Needed:
For this lesson the following materials are needed
o
o
o
Pencil
Colored Pencil
Patty Paper
o
o

Highlighter
Activities #1, #2 and #3 worksheet
Further Recommendations:
Before giving the activities to the students is important that the teacher get familiar with the content.
Additional Information/Instructions
By Author/Submitter
Resource may align with the following standards of math practice MAFS.K12.MP.1.1 - Make sense of problems and persevere in solving them.
MAFS.K12.MP.4.1 - Model with mathematics.
MAFS.K12.MP.5.1 - Use appropriate tools strategically.
MAFS.K12.MP.6.1 - Attend to precision.
MAFS.K12.MP.7.1 - Look for and make use of structure.
Use of the following GeoGebraTube resource is acknowledged: "Parallel Lines cut by
Transversal" by asewell, accessed from http://www.geogebratube.org/student/m24184, used
under Creative Common Attribution Share-Alike license:
http://creativecommons.org/licenses/by-sa/3.0/
SOURCE AND ACCESS INFORMATION
Contributed by: celia segarra
Name of Author/Source: celia segarra
District/Organization of Contributor(s): Broward
Is this Resource freely Available? Yes
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.8.G.1.5:
Description
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. For example, arrange three
copies of the same triangle so that the sum of the three angles
appears to form a line, and give an argument in terms of
transversals why this is so.