Question

use the diagram.
select all valid congruence statements.
□ a) ∠f ≅ ∠r
□ b) ∠g ≅ ∠t
□ c) overline{gh} ≅ overline{tr}
□ d) overline{st} ≅ overline{hf}
□ e) △ ghf ≅ △ trs
□ f) △ hgf ≅ △ tsr

Explanation:

Step1: Analyze triangle congruence

Since the triangles are congruent (by SSS as all corresponding sides are equal as per markings), corresponding angles and sides are congruent.

Step2: Check each option

• Option A: $\angle F$ and $\angle R$ are not corresponding angles.
• Option B: $\angle G$ and $\angle T$ are corresponding angles (from congruent triangles $\triangle HGF\cong\triangle TSR$).
• Option C: $\overline{GH}$ and $\overline{TR}$ are not corresponding sides.
• Option D: $\overline{ST}$ and $\overline{HF}$ are corresponding sides (from congruent triangles $\triangle HGF\cong\triangle TSR$).
• Option E: $\triangle GHF$ and $\triangle TRS$ - the order of vertices is wrong for congruence.
• Option F: $\triangle HGF\cong\triangle TSR$ - correct as per SSS (all sides marked equal) and vertex order.

Answer:

B. $\angle G\cong\angle T$, D. $\overline{ST}\cong\overline{HF}$, F. $\triangle HGF\cong\triangle TSR$