Which statement correctly describes the relationship between the triangles in the diagram?

Question

(1 point)
Responses

△GHJ≅△IJH
by ASA Congruence Theorem.
triangle upper G upper H upper J congruent to triangle upper I upper J upper H by ASA Congruence Theorem.

△GHJ≅△JHI
by AAS Congruence Theorem.
triangle upper G upper H upper J congruent to triangle upper J upper H upper I by AAS Congruence Theorem.

△GJH≅△JHI
by SSS Congruence Theorem.
triangle upper G upper J upper H congruent to triangle upper J upper H upper I by SSS Congruence Theorem.

△HGJ≅△HJI
by SAS Congruence Theorem.

Answer 1

To determine the correct statement, we need to analyze the congruence of the triangles based on the given options and their corresponding congruence theorems (ASA, AAS, SSS, SAS).

1. ASA (Angle-Side-Angle) – This theorem states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

2. 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 a corresponding non-included side of another triangle, then the triangles are congruent.

3. SSS (Side-Side-Side) – This theorem states that if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

4. SAS (Side-Angle-Side) – This theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Without seeing the diagram or knowing the specific measurements or angles of triangles GHJ, IJH, JHI, and HGJ, I can't definitively assess which of the statements might apply. However, I can guide you on how to analyze them based on the congruence theorems:

• Identify the angles and sides mentioned in each triangle's congruence statement.
• Check if the relationships satisfy one of the congruence theorems.

You can examine your diagram and verify the angles and sides accordingly. Once you do that, you should be able to identify which of the statements is true.