To determine which theorem can be used to prove the congruence of triangles \( \triangle GHI \) and \( \triangle GJI \), we need to analyze the specific information provided in the diagram. However, since I cannot see the diagram, I can provide general guidelines for each theorem:
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SAS Congruence Theorem: 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.
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SSS Congruence Theorem: If all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.
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AAS Congruence Theorem: 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.
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ASA Congruence Theorem: 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.
Depending on which sides and angles of triangles \( GHI \) and \( GJI \) are given as equal in the diagram, you would use one of these theorems to prove their congruence.
- If you have two sides and the included angle equal, use SAS.
- If you have all three sides equal, use SSS.
- If you have two angles and a non-included side equal, use AAS.
- If you have two angles and the included side equal, use ASA.
Please check the diagram for the specific relationships among the angles and sides to select the correct theorem.
1 answer