To determine which parallelogram is divided into two triangles that can be proven congruent by the SSS (Side-Side-Side) Congruence Theorem, we need to analyze how the parallelograms can be split into triangles.
In any parallelogram, if you draw a diagonal, it divides the parallelogram into two triangles. For instance, in parallelogram PQRS, if you draw the diagonal PS, it divides the parallelogram into triangles PQS and RSP.
In parallelograms, opposite sides are equal (PQ = RS and QR = PS), which implies:
- Triangle PQS has sides PQ and PS,
- Triangle RSP has sides RS and RP.
Since PQ = RS and QR = PS, we can conclude that the two triangles are congruent based on the SSS Congruence Theorem.
Therefore, any of the listed parallelograms (PQRS, WXYZ, JKLM, or ABCD) can be demonstrated to have congruent triangles by drawing diagonals, as long as they're parallelograms.
If you are looking for a specific answer based on a given context or a particular shape, please clarify with the context provided for each parallelogram. In general, the result holds for any regular parallelogram.