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 SSS Congruence Theorem SSS Congruence Theorem SAS Congruence Theorem

Question

the image:
The image shows a geometric figure with four points labeled ( G ), ( H ), ( J ), and ( I ). Here’s a detailed description:

Points and Labels:
( G ) is at the top of the figure.
( H ) and ( J ) are at the bottom, forming the base of a triangle.
( I ) is below the base, connected to points ( G ), ( H ), and ( J ).
Lines and Connections:
Lines connect ( I ) to ( G ), ( H ), and ( J ), forming three smaller triangles within the larger triangle ( GHJ ).
The lines ( \overline{IG} ), ( \overline{IH} ), and ( \overline{IJ} ) converge at point ( I ).
Triangles:
The larger triangle ( GHJ ) has ( G ) at the top and ( H ) and ( J ) at the base.
The smaller triangles are ( \triangle IGH ), ( \triangle IHJ ), and ( \triangle IJG ).
This figure resembles a pyramid with a triangular base when viewed in two dimensions. It could be used in geometry problems involving properties like surface areas, volumes, or angle measures.

Answer 1

To determine which theorem can be used to prove that \( \triangle GHI \cong \triangle GJI \), we need to assess the information provided about the triangles.

From the description, we can derive the following information:

1. The triangles share a common side, \( \overline{GI} \).
2. \( \angle GHI \) and \( \angle GJI \) are angles at point \( G \) which means they can be considered as part of the respective triangles.
3. \( \overline{GH} \) and \( \overline{GJ} \) are the other sides of each triangle extending from point \( G \).

Given these points, the proper theorem to use is the Angle-Side-Angle (ASA) Congruence Theorem, because we have:

• An angle in \( \triangle GHI \) (let's say \( \angle GHI \)) and an angle in \( \triangle GJI \) (let's say \( \angle GJI \)) that are both adjacent to side \( \overline{GI} \) (common side).
• The shared side \( \overline{GI} \).
• A second angle corresponding in each triangle, if applicable.

Thus, the correct answer is: ASA Congruence Theorem.