Using the congruence statement △BGH≅△PCF

Question

, which of the following statements is correct?



(1 point)
Responses

∠G≅∠C
∠G≅∠C

It is impossible to tell with the information given.
It is impossible to tell with the information given.

∠H≅∠P
∠H≅∠P

∠B≅∠F

Answer 1

The congruence statement \( \triangle BGH \cong \triangle PCF \) tells us that the corresponding angles and sides of the two triangles are equal. From this statement, we can establish the following relationships:

• \( \angle B \cong \angle P \)
• \( \angle G \cong \angle C \)
• \( \angle H \cong \angle F \)

Based on the options provided:

1. \( \angle G \cong \angle C \) - This statement is correct.
2. It is impossible to tell with the information given - This statement is incorrect.
3. \( \angle H \cong \angle P \) - This statement is incorrect.
4. \( \angle B \cong \angle F \) - This statement is incorrect.

The correct response is:

\( \angle G \cong \angle C \).