Question
What other information is needed to prove triangle ABC ≅ triangle QRS by SAS congruence theorem? (1 point) Responses <A ≅ <Q AB ≅ QR AB ≅ QR AC ≅ QS AC ≅ QS <C ≅ < S
Answers
GPT-4o mini
To prove triangle ABC ≅ triangle QRS by the SAS (Side-Angle-Side) congruence theorem, you need to establish that:
1. Two sides of one triangle are congruent to two sides of the other triangle.
2. The angle included between those two sides is congruent in both triangles.
In your options, the necessary information to confirm triangle ABC ≅ triangle QRS by the SAS theorem would be:
**AB ≅ QR** and **AC ≅ QS** along with the included angle **<C ≅ <S**.
So, the correct responses that contribute to proving the congruence by the SAS theorem would be:
- **AB ≅ QR**
- **AC ≅ QS**
- **<C ≅ <S**
Any combination of these sides and the included angle would satisfy the requirements for the SAS theorem proof.
1. Two sides of one triangle are congruent to two sides of the other triangle.
2. The angle included between those two sides is congruent in both triangles.
In your options, the necessary information to confirm triangle ABC ≅ triangle QRS by the SAS theorem would be:
**AB ≅ QR** and **AC ≅ QS** along with the included angle **<C ≅ <S**.
So, the correct responses that contribute to proving the congruence by the SAS theorem would be:
- **AB ≅ QR**
- **AC ≅ QS**
- **<C ≅ <S**
Any combination of these sides and the included angle would satisfy the requirements for the SAS theorem proof.
You can only choose one
GPT-4o mini
If you can only choose one option to prove triangle ABC ≅ triangle QRS by the SAS congruence theorem, the best choice would be:
**<C ≅ <S**
This option indicates that the included angle between the sides \(AB\) and \(AC\) of triangle ABC is congruent to the included angle between the sides \(QR\) and \(QS\) of triangle QRS. To fully establish congruence via the SAS theorem, you would also need to know that \(AB ≅ QR\) and \(AC ≅ QS\), but since only one option can be selected, choosing the included angle is key for the SAS criterion.
**<C ≅ <S**
This option indicates that the included angle between the sides \(AB\) and \(AC\) of triangle ABC is congruent to the included angle between the sides \(QR\) and \(QS\) of triangle QRS. To fully establish congruence via the SAS theorem, you would also need to know that \(AB ≅ QR\) and \(AC ≅ QS\), but since only one option can be selected, choosing the included angle is key for the SAS criterion.