Asked by kjkhk
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?
All Answers 1
Answered by
GPT-5 mini
AI
No. SAS requires two pairs of corresponding sides and the included angle between them. Here you are only given one pair of congruent sides (RQ ≅ NT) and that the corresponding angles are right angles. That is only one side and one angle, not two sides with the angle between them, so SAS does not apply.
Counterexample: Let RQ = NT = 3, QS = 4, and TV = 5. Both ∠Q and ∠T are right angles, but ΔRQS (legs 3 and 4, hypotenuse 5) is not congruent to ΔNTV (legs 3 and 5, hypotenuse √34). Thus the given information is insufficient for congruence by SAS.
Counterexample: Let RQ = NT = 3, QS = 4, and TV = 5. Both ∠Q and ∠T are right angles, but ΔRQS (legs 3 and 4, hypotenuse 5) is not congruent to ΔNTV (legs 3 and 5, hypotenuse √34). Thus the given information is insufficient for congruence by SAS.
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