Congruence Congruent Triangles

Do These Properties Guarantee Congruence?

The activity is from a Shell Center task, and the student work is from my own class. We’re missing a few kids, but this is representative of the whole group’s work.


  1. What do you notice? Anything interesting?
  2. What categories of student responses do you see?
  3. What sort of feedback would you give to push their mathematical thinking further?

Geo Y - Pre MARS Congruet Triangles-page-001Geo Y - Pre MARS Congruet Triangles-page-012 Geo Y - Pre MARS Congruet Triangles-page-014 Geo Y - Pre MARS Congruet Triangles-page-016 Geo Y - Pre MARS Congruet Triangles-page-018  Geo Y - Pre MARS Congruet Triangles-page-003 Geo Y - Pre MARS Congruet Triangles-page-005 Geo Y - Pre MARS Congruet Triangles-page-007 Geo Y - Pre MARS Congruet Triangles-page-010

2 replies on “Do These Properties Guarantee Congruence?”

The students clearly understand that congruent triangles have to have the same angles. That much is clear from all of the answers. Student #6 also indicates an understanding that “similar” and “congruent” aren’t the same thing, but is a bit fuzzy on what the difference is between the two.

The students who got the wrong answer all understand that the angles must be the same for both triangles based on the rule about the sums of angles in a triangle. But they seem to have forgotten about similarity, and that congruent triangles have to have the same side lengths, not just the same angles. Or, they may just not be thinking about the fact that nobody said anything to constrain the side lengths in the original problem.

Interesting. Don’t American schools start off by showing and proving properties of congruence and similarity?

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