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Question

WHich answer is correct and why with context clues and be smart
Question
Using the congruence statement △BGH≅△PCF
, which of the following statements is correct?



(1 point)
Responses

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

∠H≅∠P
∠H≅∠P

∠B≅∠F

∠B≅∠F


∠G≅∠C
∠G≅∠C
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Answer 1

To determine the correct statement from the congruence statement \( \triangle BGH \cong \triangle PCF \), we can use the properties of congruent triangles. When two triangles are congruent, corresponding angles and corresponding sides are equal.

The notation \( \triangle BGH \cong \triangle PCF \) indicates that:

• Vertex \( B \) corresponds with vertex \( P \)
• Vertex \( G \) corresponds with vertex \( C \)
• Vertex \( H \) corresponds with vertex \( F \)

From this, we can conclude the following relationships:

1. \( \angle B \cong \angle P \)
2. \( \angle G \cong \angle C \)
3. \( \angle H \cong \angle F \)

Now, let's evaluate the answer choices provided:

1. It is impossible to tell with the information given - This is incorrect because we can deduce relationships from the congruence statement.
2. \( \angle H \cong \angle P \) - This is incorrect since \( \angle H \) corresponds to \( \angle F \).
3. \( \angle B \cong \angle F \) - This is incorrect since \( \angle B \) corresponds to \( \angle P \).
4. \( \angle G \cong \angle C \) - This is correct since \( \angle G \) corresponds to \( \angle C \).

The correct answer is \( \angle G \cong \angle C \) because it accurately reflects the relationships established by the congruence of the two triangles.