Discovery: Congruent Triangles

My big teaching passion is Geometry, and I absolutely love to use inquiry-based learning.

Geometry is just meant to be explored and discovered in a hands-on way!

Try this investigation with your class and allow them to discover SSS, SAS, and ASA for themselves.  They will really understand and remember it!


Materials:
(for each student or pair working together)
- 2 pieces of plastic straw 4 inches long
- 2 pieces in another color that are 5 inches long
- 2 pieces in a third color that are 6 inches long
- string or yarn
- 4 paper clips

They can thread one of each length onto a piece of yarn and tie it off to create a triangle.  Challenge them to create a second triangle with the other three pieces that is NOT congruent to the first. (They discover SSS for themselves)

Next, use a paper clip to fix an angle between two straw lengths, and challenge them to again create another triangle.  Continue the process, going on to ASA and SAS. 

I like to have students record their observations by writing a conditional statement of their own explaining their discoveries for each pair of triangles.  Give them only this structure as guidance:   If ____________, then _______________.

After the hands-on investigation, have students share the rules that they wrote for congruent triangles.  Clear up any misconceptions and give notes on notation, order of vertices, etc.

I talk about why AAA and SSA are not sufficient to prove triangles congruent.  We also discuss HL and AAS.  On a block schedule, this all can fit into one class period, but on a traditional schedule, it makes sense to break congruent triangles into a couple of days.

I like to set up practice afterward in a way that leads smoothly into proof writing. 
I require them to write congruency statements, identify all the corresponding parts, and work with complex diagrams with two triangles, like they will see later on.  This helps lead them into the next steps more easily.  Here's my practice pack.

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