To determine the appropriate theorem to prove that triangle GHI is congruent to triangle GJI, we need to analyze the relationships between the angles and sides of the triangles based on the given information from the diagram.
Without seeing the diagram, I can give you a brief explanation of each theorem:
a. AAS (Angle-Angle-Side) Congruence Theorem: If two angles and a non-included side of one triangle are respectively equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
b. SAS (Side-Angle-Side) Congruence Theorem: If two sides and the included angle of one triangle are respectively equal to two sides and the included angle of another triangle, then the triangles are congruent.
c. ASA (Angle-Side-Angle) Congruence Theorem: If two angles and the included side of one triangle are respectively equal to two angles and the included side of another triangle, then the triangles are congruent.
d. SSS (Side-Side-Side) Congruence Theorem: If three sides of one triangle are respectively equal to three sides of another triangle, then the triangles are congruent.
To choose the correct theorem, check whether you have:
- Two angles and the included side (use ASA)
- Two sides and the included angle (use SAS)
- Two angles and a non-included side (use AAS)
- Or, three sides (use SSS)
If you provide specific details from the diagram such as which angles and sides are known to be equal, I can help further determine which theorem applies.
1 answer