Discovering Triangle Congruence Theorems



Click on the following triangles to sketch them using the given constraints in Geometer's Sketchpad.

Triangle Constraints

Triangle FUN Triangle CAT Triangle DOG Triangle PET Triangle TOP
FU = 2 cm CA = 8 cm Angle D = 55 deg. Angle P = 98 deg. TO = 5 cm
UN = 4 cm Angle A = 45 deg. Angle O = 30 deg. PE = 15 cm OP = 15 cm
NF = 5 cm AT = 5 cm  Angle G = 95 deg. Angle E = 20 deg. Angle P = 48 deg.

For each triangle you have constructed, try constructing another triangle with the same constraints that is not congruent to the first.

Second constructions:

Trinagle FUN
Trinagle CAT
Triangle DOG
Triangle PET
Triangle TOP

Now that you have made some observations about constructing congruent triangles, please answer the following questions:

1.    How many constraints do you need to construct a triangle?

2.    Which constraints are needed to construct congruent triangles?

3.    Which constraints do you need to construct similar triangles?

4.    Look at Triangle TOP more closely, two triangles can be constructed from theses constraints.  Construct the two triangles.
        How might we changle the construction to construct congruent triangles?

Now that we have made some observations and conclusions about congruent triangles, let's look at some common congruence theorems that we will be using to prove congruent triangles.

Congruence Theorems