Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 71782
Parallel Lines
Students will be able to prove that alternate interior angles are congruent and corresponding angles are congruent given two parallel lines and a
traversal line. Students will use GeoGebra to explore real-world images to see if they can prove that their line segments are parallel.
Subject(s): Mathematics
Grade Level(s): 7, 8, 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Computer for Presenter,
Computers for Students, Internet Connection,
Interactive Whiteboard, LCD Projector, Overhead
Projector, GeoGebra Free Software (Download the
Free GeoGebra Software)
Instructional Time: 2 Hour(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: Parallel lines, Corresponding lines, Alternate Interior angles, Alternate Exterior angles, Consecutive
Interior angles, transversal lines
Resource Collection: FCR-STEMLearn Geometry
ATTACHMENTS
Parallel Lines Summative Assessment – page 1.docx
Parallel Lines Summative Assessment – page 2.docx
Parallel Lines_Worksheet Independent Practice.docx
Parallel Lines_Worksheet Independent Practice page 2.docx
Parallel Lines Worksheet 1_WarmUp.docx
Parallel Lines Worksheet 1_WarmUp page 2.docx
Parallel Lines worksheet 3_Class Activity.docx
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?
Students will be able to:
know and label angles formed by parallel lines and transversals.
use angle relationships to prove that lines are parallel.
prove that two lines are parallel given at least 2 angles.
Prior Knowledge: What prior knowledge should students have for this lesson?
Warm-Up Activity: See Parallel Lines Worksheet 1_WarmUp, attached.
Students should be familiar with finding the slopes of lines and know the relationships of parallel lines and perpendicular lines.
Students should be familiar with identifying angle pairs formed by a transversal.
Guiding Questions: What are the guiding questions for this lesson?
What do we know about slopes and the relationships with parallel and perpendicular lines?
page 1 of 3 During the warm-up activity, ask students what they know about Consecutive Interior angles, Corresponding angles, Alternate Interior angles, and Alternate Exterior
angles.
During the Geogebra activity, ask students, "How can we determine if lines are parallel?"
During the proof writing process, ask the students if there are different ways to order the statements in the proof and still make it true.
What statements in our proof must come prior to other statements?
Teaching Phase: How will the teacher present the concept or skill to students?
Before Class Preparations:
Make sure you have access to computers a ratio of at least 1 computer to every 2 students.
Students can work in pairs or alone to complete the investigation task.
Download Geogebra to the desktop of the computer and go over some of the basic tools in Geogebra.
Constructing parallel lines and a transversal line in Geogebra
Have students open Geogebra and construct a line.
Next, have students construct a line parallel to the first line.
Students should construct a transversal line through the parallel lines.
Refer to the Parallel lines worksheet as a guide to label your angles before you begin your investigations.
Answer questions 1, 2, and 3 on the Parallel lines worksheet.
Using a Geogebra file to investigate the angles formed from two parallel lines and a transversal
An alternate activity is to use a Geogebra file that was already created and have the students move the points to see the relationship of the angles. Parallel Lines
Geogebra file
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Importing an image into Geogebra and proving that you have two parallel lines, Option 1: Student-led
You can get an image from the Internet or a photograph of an image that may contain two parallel lines.
Save the image on the computer desktop.
Open Geogebra, click on the image and open the image.
Draw two lines over the picture using the line tools.
Draw a transversal line.
Measure two angles that they can use to prove that the lines are parallel.
Have them write a proof describing how they proved or disproved that the lines are parallel or not parallel.
Option 2: Teacher-led
If unable to have students input/upload images, the teacher may wish to project this image and perform the Guided Practice through whole group setting. Students
could take turns measuring angles on the projected image.
Here is an example of an image: Geogebra file with image
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
See Parallel Lines Worksheet Independent Practice.
The Answer sheet can be found under the attachment tab.
Summative Assessment
Students will be given a short summative assessment to assess their mastery of this standard. Please see the attachments.
Formative Assessment
Warm-Up: Based on the students' ability to calculate the slopes of lines, the teacher can remediate as needed.
During the class activity, teacher will walk around and ask guiding questions to see if students understand how to construct two parallel lines and can use the
relationships of the angles formed by the transversal lines.
Feedback to Students
Students will receive feedback throughout the lesson through guided questions. The teacher can allow students to critique other students' work to give instant
feedback. Then the teacher can walk around and give individual or group feedback.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Make any accommodations according to a student's Individual Education Plan (IEP).
Students may need preferential seating.
Students may need a longer time to complete tasks.
Students may need to be paired with another student.
Suggested Technology: Computer for Presenter, Computers for Students, Internet Connection, Interactive Whiteboard, LCD Projector, Overhead Projector, GeoGebra
Free Software
Special Materials Needed:
The teacher will need to download GeoGebra on computer(s). There is also an alternate activity which you will have to give the students prior notice to bring in an
image or photograph that may have parallel lines.
Additional Information/Instructions
By Author/Submitter
page 2 of 3 This lesson aligns with the following Standards for Mathematical Practice:
MAFS.K12.MP1.1: Make sense of problems and perseveres in solving them.
MAFS.K12.MP5.1: Use appropriate tools strategically.
SOURCE AND ACCESS INFORMATION
Contributed by: Winsome Flynn
Name of Author/Source: Winsome Flynn
District/Organization of Contributor(s): Broward
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-CO.3.9:
Description
Prove theorems about lines and angles; use theorems about lines and angles to solve problems. Theorems include:
vertical angles are 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.
page 3 of 3