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Use the image to answer the 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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1 answer

To determine the congruence theorem that proves \(\triangle GHI \cong \triangle JKL\), we need to analyze the angles and sides of both triangles. However, without the specific image or details about the triangles (like which sides or angles are congruent), I can't provide a definitive answer.

Here's a brief overview of the theorems:

  1. SAS (Side-Angle-Side) Theorem: Two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

  2. SSS (Side-Side-Side) Theorem: Two triangles are congruent if all three sides of one triangle are equal to the three sides of another triangle.

  3. ASA (Angle-Side-Angle) Theorem: Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

  4. AAS (Angle-Angle-Side) Theorem: Two triangles are congruent 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.

Based on common scenarios if triangles are said to be similar, the congruence can most often be established using the side lengths if they are proportional (for SSS) or if you have an angle included (for ASA/SAS).

If you can provide specific side lengths or angles that are congruent or proportional, I could help pinpoint which theorem applies here. Please clarify with the relevant information!