Use the image to answer the question.

Question

A vertically oriented kite shape upper G upper H upper I upper J is bisected by a vertical line from upper G to upper I, dividing the kite into two equal triangles upper G upper H upper I and upper G upper J upper I. Angles are labeled.

Based on the information in the diagram, which theorem can be used to prove △GHI≅△GJI?

(1 point)
Responses

ASA Congruence Theorem
ASA Congruence Theorem

AAS Congruence Theorem
AAS Congruence Theorem

SAS Congruence Theorem
SAS Congruence Theorem

SSS Congruence Theorem
SSS Congruence Theorem

Answer 1

To prove that triangles \( \triangle GHI \) and \( \triangle GJI \) are congruent, we need to analyze the corresponding elements of the two triangles.

1. Side \( GI \) is common to both triangles, therefore it is equal.
2. Angles \( \angle HGI \) and \( \angle JGI \) are the angles formed by the vertical bisector, which are equal as they are angles on the same line.
3. Lastly, the base \( \angle GIH = \angle GJI \) if they are equal due to symmetry.

Based on this analysis, to prove the congruence of the triangles, we can apply the ASA (Angle-Side-Angle) Congruence Theorem because we have two angles and the included side being equal.

Therefore, the correct response is:

ASA Congruence Theorem