Introduction to Two-Column Proof

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SWBAT complete a two-column proof. Students will understand how the statements and justifications of a proof can be organized using a two-column format.

Big Idea

Students use triangle congruence to understand the reasoning behind an old-timer’s method for checking an assembly for ‘squareness’.

Lesson Opener

5 minutes

The purpose of the lesson opener is for students to review conditions for triangle congruence and two practice flow proofs in cooperative learning teams. 

This Lesson Opener follows our Team Warm-up format.


To introduce today’s lesson, I call the attention of the class to the flow proofs written on the front board.  I ask students if they can think of another way to organize a proof, so that a justification is provided for every statement.  I accept ideas.  Then, I tell the class that today they will be learning how to organize proofs using a table or two-column format.  I review the agenda and learning goals for the lesson.

Checking for Squareness

5 minutes

The purpose of the activity is to introduce students to the two-column format for a proof, while reviewing theorems and properties that can be used in a proof that triangles are congruent. 


I have students get white boards, rags, and dry erase markers, while I open up the web site: Practive with Beginning Congruent Triangle Proofs.  The web site can be accessed by clicking on the hyperlink in the slide show for this lesson.


I point out to the class that the 2-column format is another way to organize the statements and supporting justifications for each in a formal proof.  For today’s activity, I ask students to practice using definitions, theorems, postulates, and properties to justify the lines of the proof.  Beginning with the first line of the first proof, I have students write a justification on their white board and hold it up for me to check.   As we work through a few proofs, I pick up the pace.  Eventually, I will ask students to number their white boards with the numbers of the lines of each proof and write a justification for each line of the proof. 


I plan to work through the first three problems on the web-site.  The class will complete a fourth problem if we can do it in the time allowed. 

Completing a Two-Column Proof

20 minutes

Lesson Close

5 minutes

The lesson close asks students to summarize the procedure for checking an assembly for squareness that they investigated during the lesson.    I display the lesson close question on the front board using the slideshow.  I ask students to brainstorm in their teams before writing their answers in their learning journals.  The purpose of the learning journal is to encourage students to reflect on what they have learned (as well as to provide individual accountability).  Time permitting, I also ask one student from each team to write a team answer on the white board.  This gives me immediate feedback on what students learned from the lesson.