In the square image, G H J I

Question

Which statement correctly describes the relationship between the triangles in the diagram? (1 point) △ GJH≌ △ JHI by SSS Congruence Theorem. △ GHJ≌ △ IJH by ASA Congruence Theorem. △ HGJ≌ △ HJI by SAS Congruence Theorem. △ GHJ≌ △ JHI by AAS Congruence Theorem.

Answer 1

To determine which statement correctly describes the relationships between the triangles in the image labeled G H J I, we need to analyze their properties based on the given options.

1. △ GJH≌ △ JHI by SSS Congruence Theorem.

   • For the SSS (Side-Side-Side) Congruence Theorem, all three sides of one triangle must be equal to the three sides of the other triangle. We need to check the lengths of the corresponding sides of triangles GJH and JHI. This option can be valid if the sides are proven to be equal but we need more information on the sides.

2. △ GHJ≌ △ IJH by ASA Congruence Theorem.

   • The ASA (Angle-Side-Angle) Congruence 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, the triangles are congruent. This statement would be valid if we know two angles and the included side of both triangles are equal.

3. △ HGJ≌ △ HJI by SAS Congruence Theorem.

   • The SAS (Side-Angle-Side) Congruence 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, the triangles are congruent. This option would be valid if the corresponding sides and the included angle can be shown to be equal.

4. △ GHJ≌ △ JHI by AAS Congruence Theorem.

   • The AAS (Angle-Angle-Side) Congruence 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, the triangles are congruent. This will hold true if we can prove those conditions.

To determine which statement is correct, you would typically rely on the specific details or measures from the image involved.

However, without seeing the actual diagram comprising triangles GJH, JHI, GHJ, and IJH and their respective sides and angles, I can't definitively state which one is true. You should check each condition based on the attributes within your diagram.

To summarize: Review the properties of the triangles in the image to conclude which statement applies based on the congruence theorems (SSS, ASA, SAS, AAS) mentioned.