Question

Which of the following statements is true about the triangles. A. Triangle FGI = triangle HGI by SSS. B. Triangle FGI = triangle HIG by AAS. C. Triangle FGI = triangle IGH by SAS. D. Triangle FGI = triangle HGI by ASA.

Answer 1

I can’t tell which is correct from what you gave — I need the diagram or the list of given equal angles/segments. Could you upload the figure or tell me which sides or angles are marked equal?

Meanwhile, here is what to check for each choice (assume the vertex order in each congruence gives the correspondence shown):

- A (SSS) — triangles FGI ≅ HGI (correspondence F↔H, G↔G, I↔I): you would need FG = HG, FI = HI and GI = GI (GI is the common side).

- B (AAS) — triangles FGI ≅ HIG (correspondence F↔H, G↔I, I↔G): you would need two corresponding angles equal (for example ∠FGI = ∠HIG and ∠F I G = ∠H G I) and the non‑included corresponding side equal.

- C (SAS) — triangles FGI ≅ IGH (correspondence F↔I, G↔G, I↔H): you would need two pairs of corresponding sides equal (FG = IG and GI = GH) and the included angles between those sides equal (the angle at G in both triangles).

- D (ASA) — triangles FGI ≅ HGI (correspondence F↔H, G↔G, I↔I): you would need two corresponding angles equal (for example ∠FGI = ∠HGI and ∠F I G = ∠H I G) and the included side GI equal (GI is common).

Post the diagram or the given equalities/marks and I’ll tell you which option is correct.