Question

triangles rqs and ntv have the following characteristics: • right angles at ∠q and ∠t • rq ≅ nt can it be concluded that δrqs ≅ δntv 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:

SAS congruence requires two pairs of congruent sides and the included angle. Triangles RQS and NTV have right angles (included angles) at Q and T, and one pair of congruent sides RQ ≅ NT. But SAS needs a second pair of adjacent sides to the right angle to be congruent (e.g., QS ≅ TV or QR ≅ NT and QS ≅ TV). Only one side pair is given, so SAS can’t be concluded.

Answer:

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