Developing Congruence Criteria (SSA)
STEP 0
The goal of this activity is to determine if we can conclude that two triangles are congruent with only some information about their sides and angles.
In order to show that they are congruent, we will attempt to map one onto the other, by mapping each vertex onto its corresponding vertex, one at a time.
STEP 1
Several segments and angles are measured in the triangles below. Does this diagram illustrate an example of SAS Congruence? Explain why / why not.
STEP 2
We will begin by making sure that vertex A corresponds with vertex J. Using the same diagram above, construct a vector to map A onto J then translate ABE along that vector.
STEP 3
The figures, after the translation performed in step 2, are shown in the box below. Next, we will try to make a second set of vertices map onto one another. Which vertices are already coinciding? Why does this make sense?
STEP 4
Is there a transformation that will allow us to make E' coincide with I? Explain.
STEP 5
We have shown that two triangles that have two pairs of congruent sides and a pair of (NON-INCLUDED) congruent angles cannot be mapped onto one another. What does this mean about two triangles that meet the SSA criteria?