Question

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 \\(\delta rqs \cong \delta ntv\\) by sas? why or why not?

yes, one set of corresponding sides and one corresponding angle are congruent.
yes, they are both right triangles.
no, it is necessary to know that another set of corresponding sides is congruent.
no, it is not possible for the triangles to be congruent.

Explanation:

Identify given geometric properties

Using the Right Triangle Definition knowledge point

$$
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Analyze SAS Congruence requirements

Using the SAS Congruence Postulate knowledge point

$$
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Determine the correct conclusion

Since the second set of corresponding sides (\(\overline{QS}\) and \(\overline{TV}\)) is not given as congruent, we cannot conclude congruence by SAS. Thus, we need to know that another set of corresponding sides is congruent.

Answer:

• Yes, one set of corresponding sides and one corresponding angle are congruent.
• Yes, they are both right triangles.
• No, it is necessary to know that another set of corresponding sides is congruent. (Correct answer)
• No, it is not possible for the triangles to be congruent.