Investigate congruence by manipulating the parts (sides and angles) of a triangle. If you can create two different triangles with the same parts, then those parts do not prove congruence. Can you prove all the theorems?
For every arrangement of three elements, it is possible to test for
triangle congruence. However, just like two triangle might be mirror
images but still congruent, flipping the order creates identical
possible theorems. For example Angle – Angle – Side is the same as
Side – Angle – Angle because they are the same elements in reverse
How many possibilities are there? Test each of them and organize your results in the table with three columns:
As you work, remember to try every possibility. When creating your
second triangle, see if an element can connect to adjacent elements in
more than one place. Also remember, you may have to turn or flip your
triangles to see how they are congruent. For example, all the triangles
to the right are congruent.
Did all the possibilities work? How are you certain of your
answers? Try comparing your answers to a friend's. If you disagree on
any possible theorem, try re-creating your triangles.