Question

Question:Use the image to answer the question.A rectangle $GHIJ$ is plotted on a grid. A diagonal line is drawn from $H$ to $J$, forming two triangles: $\triangle GHJ$ and $\triangle IJH$.Vertex $G$ is in the upper left corner, vertex $H$ is in the upper right, vertex $I$ is in the lower right corner, and vertex $J$ is in the lower left.$\angle GJH$ and $\angle JHI$ are marked with a single congruent arc.$\angle GHJ$ and $\angle HJI$ are marked with double congruent arcs.Sides $GJ$ and $HI$ measure 3 units each.Sides $GH$ and $JI$ measure 2 units each.Which statement correctly describes the relationship between the triangles in the diagram?(1 point)Multiple Choice Options (Responses)( ) $\triangle GHJ \cong \triangle JHI$ by AAS Congruence Theorem.( ) $\triangle GJH \cong \triangle JHI$ by SSS Congruence Theorem.( ) $\triangle GHJ \cong \triangle IJH$ by ASA Congruence Theorem.( ) $\triangle HGJ \cong \triangle HJI$ by SAS Congruence Theorem.

Answer 1

Answer: ( ) triangle GHJ ≅ triangle IJH by ASA Congruence Theorem.

Reason: ∠GHJ ≅ ∠HJI and ∠GJH ≅ ∠JHI, and the included side HJ is common to both triangles, so the triangles are congruent by ASA.