Question
Based on the information in the diagram, which theorem can be used to prove △GHI≅△GJI ? (1 point) Responses SAS Congruence Theorem SAS Congruence Theorem SSS Congruence Theorem SSS Congruence Theorem ASA Congruence Theorem ASA Congruence Theorem AAS Congruence Theorem
Answers
GPT-4o mini
To determine which theorem can be used to prove △GHI ≅ △GJI, we need to consider the information typically used for triangle congruence:
1. **SAS (Side-Angle-Side) Congruence Theorem**: Two triangles are congruent if two sides and the included angle of one triangle are respectively equal to two sides and the included angle of another triangle.
2. **SSS (Side-Side-Side) Congruence Theorem**: Two triangles are congruent if all three sides of one triangle are equal to all three sides of another triangle.
3. **ASA (Angle-Side-Angle) Congruence Theorem**: Two triangles are congruent if two angles and the included side of one triangle are respectively equal to two angles and the included side of another triangle.
4. **AAS (Angle-Angle-Side) Congruence Theorem**: Two triangles are congruent if two angles and a non-included side of one triangle are respectively equal to two angles and a corresponding non-included side of another triangle.
To accurately select the correct theorem, I would need more details about the specific sides and angles provided in your diagram or a description of the triangle relationships. However, here's a guideline on how to use the options based on typical cases:
- **If two sides and the included angle are known**: Use **SAS**.
- **If all three corresponding sides are known**: Use **SSS**.
- **If two angles and the included side are known**: Use **ASA**.
- **If two angles and a non-included side are known**: Use **AAS**.
If you can provide more details from the diagram, I can help you choose the appropriate theorem more accurately!
1. **SAS (Side-Angle-Side) Congruence Theorem**: Two triangles are congruent if two sides and the included angle of one triangle are respectively equal to two sides and the included angle of another triangle.
2. **SSS (Side-Side-Side) Congruence Theorem**: Two triangles are congruent if all three sides of one triangle are equal to all three sides of another triangle.
3. **ASA (Angle-Side-Angle) Congruence Theorem**: Two triangles are congruent if two angles and the included side of one triangle are respectively equal to two angles and the included side of another triangle.
4. **AAS (Angle-Angle-Side) Congruence Theorem**: Two triangles are congruent if two angles and a non-included side of one triangle are respectively equal to two angles and a corresponding non-included side of another triangle.
To accurately select the correct theorem, I would need more details about the specific sides and angles provided in your diagram or a description of the triangle relationships. However, here's a guideline on how to use the options based on typical cases:
- **If two sides and the included angle are known**: Use **SAS**.
- **If all three corresponding sides are known**: Use **SSS**.
- **If two angles and the included side are known**: Use **ASA**.
- **If two angles and a non-included side are known**: Use **AAS**.
If you can provide more details from the diagram, I can help you choose the appropriate theorem more accurately!