## Reflection: Transitions Discovering Triangle Congruence Shortcuts - Section 3: Debrief/Notes: Triangle Congruence Shortcuts

In the past, I have debriefed this investigation by passing out note takers to students, asking questions about what kinds of observations and conjectures students had made, and facilitating a whole-class discussion about the key ideas of the investigation—in this case, which constructions produced one distinct triangle and which did not.  This discussion can be a bit dissatisfying in that there are times when it feels that I, the teacher, am the one who gives all the answers.

This year, I tried something slightly different.  I passed out the note takers to students after they had finished the investigation with their partner and asked them to try to summarize their thinking on the notetaker.  This is a shift from what I have done in the past, and a good one, I think.  By giving students six pairs of triangles that show all six of the triangle shortcuts, I enabled my students to critically examine the triangles’ given information (to distinguish SAS from SSA, for example) in order to formally record their conjectures.  Furthermore, in the case of ASA, for example, students had to draw on prior knowledge in order to make a decision about whether the shortcut guarantees triangle congruence (if two angles in one triangle are congruent to two angles in another, then the third angles are congruent, thus allowing students to rely on their understanding of AAS as a congruence shortcut).

The idea of giving students time to think, do some sense making, and make some connections BEFORE facilitating a whole-class debrief discussion is not new.  However, this small decision reminded me that even the smallest decisions (giving students more think time) can increase cognitive demand and encourage higher order thinking as students construct viable arguments and critique their partner’s reasoning.

Thoughts on How to Jump into the Debrief
Transitions: Thoughts on How to Jump into the Debrief

# Discovering Triangle Congruence Shortcuts

Unit 7: Discovering and Proving Triangle Properties
Lesson 4 of 10

## Big Idea: Through construction, students will work in pairs to test "shortcuts" to use when proving triangles congruent.

Print Lesson
17 teachers like this lesson
Standards:
Subject(s):
Math, Geometry, Triangles, reasoning and proof, Triangle Congruence, triangle similarity
60 minutes

### Jessica Uy

##### Similar Lessons

###### Analyzing the Symmetry of a Polygon
Geometry » Congruence and Rigid Motions
Big Idea: Students use the symmetry of a polygon to deduce its properties while continuing to develop their ability to use transformations. Now, just where does that line of symmetry have to be?
Favorites(2)
Resources(27)
Ault, CO
Environment: Rural

###### AAS and ASA Fun
Geometry » Tremendous Triangles
Big Idea: Students will work with a partner to discover two more theorems as they explore why ASA and AAS congruence proves triangles are congruent.
Favorites(4)
Resources(22)
Saratoga Springs, NY
Environment: Suburban

###### Rigid Motion, Congruent Triangles, and Proof
Geometry » Polygons and Congruent Triangle Proofs
Big Idea: Using the method of flow chart proofs, students begin to develop the skills necessary to understand and create congruent triangle proofs.
Favorites(5)
Resources(14)
Amsterdam, NY
Environment: Urban