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.

Question

The diagram shows that ∠HGI≅∠JGI
and ∠GIH≅∠GIJ
. What additional congruence statement can be made based on the diagram?

Option #1: ∠H≅∠J


Option #2: GI¯¯¯¯¯¯¯≅GI¯¯¯¯¯¯¯


Option #3: HI¯¯¯¯¯¯¯≅JI¯¯¯¯¯¯


Option #4: GH¯¯¯¯¯¯¯¯≅GJ¯¯¯¯¯¯¯


(1 point)
Option #

Answer 1

Based on the given information and the congruences provided (∠HGI ≅ ∠JGI and ∠GIH ≅ ∠GIJ), we can further conclude the following:

Since the triangles GHI and GJI share the side GI and the angles are congruent, we can apply the Angle-Angle (AA) criterion for triangle congruence. This leads us to conclude that triangles GHI and GJI are congruent.

From the congruence of the triangles GHI and GJI, we can then state that the corresponding sides are equal. Particularly, since GHI ≅ GJI, we can deduce that the sides opposite the equal angles are also equal:

Thus, the additional congruence statement that can be made based on the diagram is:

Option #3: HI ≅ JI

So, the correct answer is Option #3.