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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

SSS Congruence Theorem
SSS Congruence Theorem

AAS Congruence Theorem
AAS Congruence Theorem

SAS Congruence Theorem
SAS Congruence Theorem
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Answer 1

To determine which theorem can be used to prove that triangles \( \triangle GHI \) and \( \triangle GJI \) are congruent, we need to analyze the properties of the kite and the information provided.

In a kite:

1. The two pairs of adjacent sides are equal.
2. The diagonals intersect at right angles.
3. The diagonal that bisects the kite divides it into two congruent triangles.

Since the vertical line from \( G \) to \( I \) bisects the kite and the angles at point \( I \) and the sides \( GI \) are equal in both triangles:

• \( GH = GJ \) (equal legs of the kite),
• \( GI = GI \) (common side),
• \( \angle GHI = \angle GJI \) (vertical angles).

Thus, we can use the SAS (Side-Angle-Side) Congruence Theorem, as we have two sides and the included angle of each triangle congruent.

Therefore, the correct response is:

SAS Congruence Theorem