ALEX Lesson Plan

     

Triangle Congruence with Rigid Motions

You may save this lesson plan to your hard drive as an html file by selecting "File", then "Save As" from your browser's pull down menu. The file name extension must be .html.

  This lesson provided by:  
Author:Morgan Boyd
Organization:Retirement
  General Lesson Information  
Lesson Plan ID: 35593

Title:

Triangle Congruence with Rigid Motions

Overview/Annotation:

This lesson will provide instruction on proving triangles to be congruent using rigid motions. Using the concept of transformations, the students will be able to manipulate the triangle on the coordinate plane. When using the coordinate plane to test congruence, the triangle or other object will slide, rotate, or flip to map onto the other object. Sometimes, the student will use a combination of the transformations. 

This lesson results from the ALEX Resource Gap Project.

 

 Associated Standards and Objectives 
Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 9-12
Geometry
8 ) Explain how the criteria for triangle congruence, angle-side-angle (ASA), side-angle-side (SAS), and side-side-side (SSS), follow from the definition of congruence in terms of rigid motions. [G-CO8]


Alabama Alternate Achievement Standards
AAS Standard:
M.G.AAS.HS.8- Given two congruent triangles and angle measures of one of the triangles, identify the angle measures of the other triangle.


Local/National Standards:

 

Primary Learning Objective(s):

The student will be able to explain the techniques of transformations to prove triangles congruent.

The student will be able to prove triangles congruent by SSS, ASA, SAS or AAS.

Additional Learning Objective(s):

The student will be able to explain the differences of each type of transformation.

The student will be able to combine transformations to prove triangles are congruent.

 Preparation Information 

Total Duration:

31 to 60 Minutes

Materials and Resources:

PowerPoint Presentation that will explain step by step during the class: "Congruent Triangles" (see attached presentation)

Pencils

Notebook paper

Scissors (if necessary)

Graph Paper (see attached file, make copies as needed)

Exit Slip Transformations with Answers (see attached file make copies for all students)

"SSS, SAS, ASA, and AAS congruences combined" and "All transformations combined" from Kuta Software (make copies for each student)

https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-congruence/v/finding-congruent-triangles

http://www.watchknowlearn.org/Video.aspx?VideoID=18777

Technology Resources Needed:

Desktop computer with PowerPoint software

Projector and/or interactive whiteboard for displaying videos and PowerPoint

iPad, Chromebook, or MacBook for students to revisit websites used in class

Websites:

Khan Academy "Congruent Triangles"-https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-congruence/v/finding-congruent-triangles

Watch Know Learn- http://www.watchknowlearn.org/Video.aspx?VideoID=18777

Kuta Software (worksheet generator)- https://www.kutasoftware.com/freeige.html. The triangle congruence and transformation worksheets are on this page. The worksheets will open in another tab. 

Background/Preparation:

Teacher:

The teacher will preview the PowerPoint presentation. The teacher needs to visit the website Kuta Software. Kuta Software has free worksheets that can be printed and copied. The teacher needs to preview the videos to determine when to stop and ask questions.

Student:

The student needs to be able to graph points on the coordinate plane. The student needs to be familiar with transformations and how triangles can be congruent. The three transformations are translation, reflection, and rotation. Three common ways to prove triangle congruence are as follows: Side-Side-Side, Side-Angle-Side, and Angle-Side-Angle.

  Procedures/Activities: 

Before:

1. As students are entering the room, the teacher will start the PowerPoint presentation on the interactive whiteboard. The first slide is the bell ringer.

2. After three or four minutes has passed, the teacher will start the slides. The students will check their answers and make corrections.

During:

1. After the definitions, the teacher will begin the video from Khan Academy. (https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-congruence/v/finding-congruent-triangles)

2. The teacher can solicit comments and questions from the students. This will be the informal assessment.

3. As the video is finishing, the teacher will pass out the practice sheets for triangle congruence from Kuta Software in the materials section. (https://www.kutasoftware.com/freeige.html) The worksheet is the following: SSS, SAS, ASA, and AAS congruences combined.

4. The teacher will monitor the students as they are working and give one-on-one guidance. The teacher can place the students in groups to allow collaboration. Using their internet capable devices, the students can revisit the websites to look at examples. A peer-tutor will be very helpful for intervention. According to the explanation, the students may have different answers for congruence. The student must identify all the parts that are corresponding.

5. The teacher will review the answers to the practice sheet.

6. The teacher will begin the video from Watch Know Learn for transformations. (http://www.watchknowlearn.org/Video.aspx?VideoID=18777)

7. As the video is finishing, the teacher will pass out the practice sheet on transformation from Kuta Software. (https://www.kutasoftware.com/freeige.html) (All transformations combined)

8. The teacher will monitor student engagement and make an informal assessment. The teacher can place the students in groups to allow collaboration.  If students need to use hands-on examples, then the students can cut out triangles and move them on the graph paper.  Using the devices, the students can revisit the websites to look at examples. A peer-tutor will be very helpful for intervention. According to the explanation, the students may have different answers for congruence. The student must identify all the parts that are corresponding.

9. The teacher will call on random students to answer selected problems. If students have questions, then the teacher will explain solutions.

After:

The teacher will pass out the exit slip called “Exit Slip Transformations with Answers”. The students will turn in the exit slip as they leave the classroom. The exit slip will be the formal assessment.



Attachments:
**Some files will display in a new window. Others will prompt you to download.
  Assessment  

Assessment Strategies

Informal:

The teacher can monitor student work as he/she walks around the room during the practice sheets. The teacher can ask questions to see if the students understand the material and the directions. The teacher will review the practice sheets with the whole class and wait for questions and comments.

Formal:

The teacher will grade the exit slip.

Acceleration:

The teacher will assign the following prompt to the accelerated students: "Explain why 'dilation' is considered a type of transformation and make an illustration to justify your answer." The student should explain that shapes being dilated are similar and the shape gets larger by a scale factor. 

Intervention:

Students requiring intervention can be provided with one-on-one instruction. As the students work in groups, the teacher can reduce the number of problems or the teacher can extend the time for the assignment. The students may also revisit the videos for extra guidance. The teacher can allow the students to cut out triangles and move them manually on the graph paper.


View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.