Congruent Triangles Lesson

Triangle Congruence 

STANDARDS (Geometry Congruence)

G-CO

6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

INTRODUCTION

In the beginning of Module 6, we learned about Rigid Transformations (translation, rotation, and reflection) and the characteristics of polygons (diagonals, symmetry, and rotational symmetry). In this lesson, we will study congruent triangles, which are triangles that simply undergo a rigid transformation.  We will learn how to prove congruent triangles with the postulates SSS, ASA, SAS, and AAS.

Extra links for transformations: 

Kahn Academy  for video tutorials with practice problems

Math Warehouse for interactive demonstrations

Math is Fun

You Tube Video  (3 minutes)

 Extra links for symmetry and rotational symmetry:

Math is Fun

Kahn Academy for video tutorials with practice problems

    

TASK

There are three tasks to complete in this lesson:

LEARN 

 Study the information on Congruent Triangles and participate in an activity

REPRODUCE

  Show your understanding of Congruent Triangles

EXPLORE

 Take it a step further and examine how Congruent Triangles are applied in the real world

LEARN  (Individual Work)

1) Visit these websites to learn about the postulates for Congruent Triangles.

How to Find if Triangles are Congruent

·       Congruent Triangles

·        

2) Answer these questions regarding what you have learned, and turn in your answers to me through Google Drive. (5pts)

1.                                  a) Describe the difference between the postulates ASA and AAS.

2.                                 b)  Why doesn't Angle-Angle-Angle work as a postulate to prove triangle                                           congruence? Show an example.

REPRODUCE    (Group Work)

There are many videos made by students and teachers that explain different math ideas.

Here are a few examples:

Direct Demonstration

        Parody/skit with songs  

·         

Music Videos  

Now it is your turn to create a video to teach the subject of Congruent Triangles!  Work in a group of no more than 4 people to create an interesting way to present the information. Choose one of these formats for your video.

• ·         Music Video - If you are musically inclined, you can write your own song, or you may use the tune of a popular song and write the lyrics to teach the viewer. Turn in a copy of the lyrics.
• 
  
• ·         Animation - You can create an animation with drawings, claymation, or computer graphics. Tell a story with characters and a plot. Turn in a copy of your storyboard.
• 
  
• ·         Interview -  Pretend you are a famous Mathematician (can be a real person or fictional) and you are being interviewed for you new discovery of congruent triangles. The interviewer can pretend to be a real talk show host (ex. Ellen, Jimmy Kimmel, or members of The View, etc.). Turn in a copy of your script.   

Your audience should watch this video and will be able to answer:

1.        What are congruent triangles?

2.       How do you prove triangles are congruent by SSS, SAS, ASA, and AAS?

EXPLORE  (Individual Work)

Here is where we find out why we need to learn this in the first place. How might someone use congruent triangles in their job?

1.      Find and contact someone who works in a profession where they need to use any of the postulates. Here are just a few examples: physicist, civil engineer, architect, graphics or software engineer, artist, carpenter, field surveyor, etc.  You may contact them through email, phone, or a visit.
2.           Interview Questions (please add more if you think of any):

a)      What is your job description? (How does your boss know you're doing your job?)

b)       How do you use congruent triangles in your work?

c)       What tools, if any, do you use when you are applying congruent triangles?

d)      What do you like best about your job, and what is the toughest part about your job?

       3.      Present this information in a slide format (Powerpoint, Google Slide, Prezi, etc.) Be                   sure to include:

a) Information such as the person's name, job title, date of interview, and type of correspondence.

b) At least 2 images.

RUBRIC Rubric for REPRODUCE		Total: 20 points
	3	2	1	0
Context	Lyrics, story, or script is very clear and relates to the Congruent Triangles accurately.	Lyrics, story, or script mostly clear and relates to Congruent Triangles accurately.	Lyrics, story, or script is unclear and does not relate to Congruent Triangles.	There is no lycrics, story or script.
Congruent Triangles (double points)	A clear and accurate definition of Congruent Triangles is included.	A mostly clear and mostly accurate definition of Congruent Triangles is included.	Congruent Triangles is added with an incorrect or unclear definition.	Congruent Triangles is not defined.
Postulates (SSS, SAS, ASA, AAS) (double points)	All Postulates are included correctly.  Extra information is added.	Many postulates are included correctly.	Postulates are included with some mistakes.	Postulates are not included.
Production Quality	Everything is clear: ie. sound, visuals, graphics, and lighting. Characters and/or storyline is easy to recognize or understand.	Most things are clear (sound, visuals, graphics, or lighting) and easy to understand, but some parts are unorganized.	Unable to hear, see, or understand some parts. Not very organized. Many editing errors.	Cannot understand the information presented.
Creativity	Video interesting and creative. Nicely and uniquely designed.	Video is interesting. Presentation is nicely designed.	Video is generic. Has some interesting parts.	Video lacks creativity.
Rubric for EXPLORE		Total: 20 points
	3	2	1	0
Background Information: Name, date of interview, job title, and type of correspondence.	Included all four pieces of information.	Missing one of the pieces of information.	Missing two or three of the four pieces of information.	Did not include any of the information.
Job Description and opinion of work. (double points)	Shows a clear understanding of the professional's job, and the pros and cons of their work.	A mostly clear understanding of the professional's job, and the pros and cons of their work.	Shows some understanding of the professional's job, and the pros and cons of their work.	Has no understanding of the professional's job, and the pros and cons of their work.
Postulates (SSS, SAS, ASA, AAS) (triple points)	All Postulates are included correctly.  Extra information is added.	Many postulates are included correctly.	Postulates are included with some mistakes.	Postulates are not included.
Presentation	Everything is easy to read and neatly displayed.  There are no spelling or grammatical errors.	Everything is easy to read, but not organized. There are only one or two spelling or grammatical errors.	Unable to read some parts. Not very organized. Many spelling or grammatical errors.	Cannot understand the information presented.

CONCLUSION

Once you have discovered how to prove congruent triangles, you will begin to see and appreciate them everywhere. The triangle is the foundation for any type of support in construction, and also found in nature. Your spatial recognition will improve with practice in Geometry, as well as your ability to support statements with justification.