Proving Triangles Congruent

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Objective

SWBAT complete a flow proof to show that triangles are congruent. Students will understand the combinations of equal side and angle measures that guarantee triangles to be congruent.

Big Idea

Using flow diagrams to organize an argument highlights conditions for triangle congruence.

Lesson Opener

10 minutes

The purpose of the lesson opener is to get students to recall the conditions required to prove triangles congruent and to refer to the applicable theorem by name.  In addition, I want all students to recall how to write a flow proof.

As students are entering the classroom, I display the lesson learning targets and agenda using the slideshow (ProvingTrianglesCongruent_Slideshow.pptx).  When the bell rings, I display the lesson opener and ask students to begin on the problem.

This is a classroom routine, so students know what to do.  A reminder is provided in the presentation.  For more information how I conduct this lesson opener, check out the Strategies folder under my Geometry curriculum on the Better Lesson web site.

When all teams have finished writing their answers to the lesson opener, I award points by writing a score next to each team’s answer and circling it.  I award one point for teamwork, one for writing a congruence statement and naming a theorem that applies.   Students are required to agree on a team answer, which encourages them to justify their answers to one another (MP3).    Writing the points on the board helps to get students to read the other teams’ answers.

By calling the class’s attention to one of the team’s answers on the board, I review with the class how to write a flow proof.  My students have used flow diagrams in the previous unit to prove that triangles are similar, so I am confident that at least one team will use a flow proof in their solution.  If none does, I am prepared to ask how we could use a flow proof to organize our thinking and present our justification in this case.  Then, I will ask for a volunteer, or I will follow the class’s instructions (in answer to my questions) to demonstrate the proof myself.

35 minutes

Introduction to Two-Column Proof

10 minutes

This activity is planned for the next lesson.  However, I will use it here if practicing flow proofs begins to get stale or as a sponge if the class moves more quickly.  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:Practice 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.

Lesson Close

5 minutes

The lesson close asks students to show that two triangles are congruent by naming the theorem that applies.    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.