To determine the correct relationship between the triangles △GJH and △JHI based on the given options, we need to analyze which congruence theorem applies. The options include SSS (Side-Side-Side), SAS (Side-Angle-Side), and AAS (Angle-Angle-Side) congruence theorems.
- SSS (Side-Side-Side): This theorem states that if all three sides of one triangle are equal to the corresponding three sides of another triangle, then the triangles are congruent.
- SAS (Side-Angle-Side): This theorem states that if two sides of one triangle and the angle between them are equal to two sides of another triangle and the angle between them, then the triangles are congruent.
- AAS (Angle-Angle-Side): This theorem states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
To select the correct statement, we would need to know the measurements of the sides and angles of the triangles. If the congruence of the triangles is based on sides and angles as per the options given, your choice would depend on what is provided in the image.
If you see that:
- All three sides of both triangles are equal, then the correct choice would be "△GJH≅△JHI by SSS Congruence Theorem."
- If two sides and the angle between them are equal, then the correct choice would be "△GJH≅△JHI by SAS Congruence Theorem."
- If two angles and a non-included side are equal, then the correct option would be "△GJH≅△JHI by AAS Congruence Theorem."
Without the specific image or measurements, we cannot definitively choose one. Please refer to the given data in the image to make your selection accordingly.