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. [br][br]In order to show that they are congruent, we will attempt to map one onto the other, by [b][u]mapping each vertex onto its corresponding vertex, one at a time.[/u][/b]

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

To determine if the triangles are congruent, we will begin by making sure that vertex A corresponds with vertex J. Using the diagram above, construct a vector to map A onto J then translate [math]\Delta[/math]ABE along that vector.

STEP 3

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? Is it possible to map all vertices onto their corresponding vertices?

STEP 4

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?