Question

triangles rqs and ntv have the following characteristics: right angles at ∠q and ∠t, rq ≅ nt. can it be concluded that △rqs ≅ △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:

Step1: Recall SAS congruence criterion

The SAS (Side - Angle - Side) congruence criterion states that for two triangles to be congruent by SAS, two pairs of corresponding sides and the included angle between them must be congruent.

Step2: Analyze given information

We know that $\angle Q=\angle T = 90^{\circ}$ and $\overline{RQ}\cong\overline{NT}$. But we only have one pair of corresponding sides and one pair of corresponding angles. For SAS, we need another pair of corresponding sides where the right - angle is the included angle.

Answer:

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