Question

Use the image to answer the 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**