Organizing and Venn Diagrams with Congruent Triangles
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Activity for reinforcing the methods of proving triangles congruent.
 

Goal:  The goal of this activity is to see if students can examine marked diagrams and determine which method of proving triangles congruent should be used.  In addition, students should recognize that there may be more than one method that may work.

(There are several variations to parts of this activity that will be mentioned along the way.)

Audience:  Students can work independently or in small groups.  This could also be a teacher-led class demonstration.

Preparation of Materials:

Assemble all of the following pieces for each student or group of students.  The pieces can be placed in an envelope or a sandwich baggie.  Ask students not to write on the pieces so that they can be used again with other classes.

1.  On one sheet of paper, list the five methods of proving triangles congruent in large print or a large font.  (ASA, SAS, SSS, AAS, HL)

Be sure that the print is large.  Each of these sections will be cut apart and used as a heading for a category.  In an attempt to conserve paper, squeeze as many repetitions of the headings as possible onto one page.  Duplicate this page so that each group of students (or each student) will have one set of the 5 methods.

(If you do not want to cut out these pieces, have students place 5 pieces of paper (or half sheets of paper) on their desks.  Labeling the 5 methods on a larger piece of construction paper will also work.)

2.  On several other sheets of paper, prepare drawings which show two triangles and their markings.  These drawings do not need to be very large. 
They should be less than the size of a 3 x 5 card. 

These drawings can be hand drawn, copied from an old worksheet, or prepared on the computer.  Create a dozen or more drawings to be used by each student or group.   For example:

3.  Also supply each student with slips of paper to be used should a duplicate listing occur.  Ask students to copy diagrams on the slips of paper should a duplicate be needed.  You will need new duplicates slips for each class.
 

Student Task:  With the category headings cut apart and the drawings cut apart, the activity is ready to begin.  Ask the students to arrange the 5 methods of proving triangles congruent across the top of their desk or table.  They are then to match the drawings with the appropriate headings, placing the triangles under a heading.

As the students may discover, several of the drawings could fit more than one category.  For example, the last figure above could be categorized as SSS or SAS.   If a duplicate is needed, ask the students to copy that diagram onto one of the duplicate slips and place it under as many headings as needed.


Alternate Idea:

Instead of using the headings, you may want to try a Venn diagram approach.  This idea could also be a follow-up to the activity described above.  Give each student or group a Venn diagram sheet for classifying overlapping drawings.  Be sure that the diagram is large and will allow for the placing of the triangle pieces.  The labels on the Venn diagram will depend upon the drawings you have chosen to use for your activity.  You may want to limit your methods to three choices to avoid confusion in the placement of the triangles.  Be sure to choose triangles that will complement the Venn diagram choices.