Question

triangle congruence: sas
triangles rqs and ntv have the following characteristics:

• right angles at \\( \angle q \\) and \\( \angle t \\)
• \\( \overline{rq} \cong \overline{nt} \\)

can it be concluded that \\( \triangle rqs \cong \triangle ntv \\) by sas? why or why not?
yes, one set of corresponding sides and one
corresponding angle are congruent.
no, it is not possible for the triangles to be
congruent.
yes, they are both right triangles.
no, it is necessary to know that another set of
corresponding sides is congruent.

Explanation:

The SAS (Side - Angle - Side) congruence criterion requires two sides and the included angle of one triangle to be congruent to the corresponding two sides and included angle of another triangle. Here, we know \( \overline{RQ}\cong\overline{NT}\) and \( \angle Q\cong\angle T\) (right angles). But for SAS, we also need the other sides adjacent to the right angles (\(QS\) and \(TV\)) to be congruent. Since we don't know if \(QS\cong TV\), we can't apply SAS.

Answer:

No, it is necessary to know that another set of corresponding sides is congruent.