Use the image to answer the question.

Question

Two similar triangles, upper G upper H upper I and upper J upper K upper L are marked for congruence.

Which congruence theorem proves △GHI≅△JKL ?

(1 point)
Responses

SAS Theorem
SAS Theorem

SSS Theorem
SSS Theorem

ASA Theorem
ASA Theorem

AAS Theorem
AAS Theorem
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Answer 1

To determine which congruence theorem proves that triangle \( \triangle GHI \cong \triangle JKL \), we need to consider the information typically provided about similar triangles.

1. SAS Theorem (Side-Angle-Side): This theorem 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.

2. SSS Theorem (Side-Side-Side): This theorem states that if all three sides of one triangle are proportional to all three sides of another triangle, then the triangles are congruent.

3. ASA Theorem (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.

4. AAS Theorem (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.

In the case of similar triangles, if it is given or demonstrated that sides are proportional and angles are equal, then it's also important to know what specific information is provided about the triangles.

If angles \( G \), \( H \), and \( I \) correspond to angles \( J \), \( K \), and \( L \), and we have the information regarding sides being proportional, the SAS or SSS theorems would apply.

To accurately answer which specific theorem is applicable, please provide information regarding the angles or the relationships of the sides between the triangles. However, if it is understood that angles are given, typically the AAS or ASA theorems are likely candidates.

Given that \( \triangle GHI \) and \( \triangle JKL \) are stated to be similar, if we only have proportional sides and angles, either the SAS or SSS could be applicable, while AAS or ASA could potentially not apply.

If I were to take a guess without the image, I would say the SAS Theorem or SSS Theorem is likely involved if there's sufficient information about sides being proportional and angles being equal.

If I had to pick one response based solely on similarity, I would lean towards SAS Theorem, as it often comes up with proving similarity as a first step leading to congruence.

So the most fitting response with this provided summary is: SAS Theorem