To determine which congruence theorem proves that triangles \( \triangle GHI \cong \triangle JKL \), we need to analyze the properties of similar triangles.
-
SAS (Side-Angle-Side) Theorem: This states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are congruent.
-
SSS (Side-Side-Side) Theorem: This states that if all three sides of one triangle are proportional to all three sides of another triangle, then the triangles are congruent.
-
ASA (Angle-Side-Angle) Theorem: This states that if two angles and the side between them of one triangle are equal to two angles and the side between them of another triangle, then the triangles are congruent.
-
AAS (Angle-Angle-Side) Theorem: This 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.
Since we are talking about similar triangles, we can conclude that the angles are equal. Therefore, if they share corresponding angles and we can prove that one pair of sides are in proportion, we can use either the SAS or the AAS theorem.
Given that the question asks specifically for a congruence theorem, and if you have confirmed that the triangles are similar, you likely have information about either sides or angles.
If there are equal angles and a good ratio of the sides, it would be likely proving via SAS or AAS. If any specific sides are compared with angles, that would solidify your theorem.
Without the image, if their sides are proportional and an angle in between them is also equal, I would likely lean towards the SAS Theorem.
Answer: SAS Theorem