Question

using the congruence statement BGH is congruent with PCF, which of the following statements is correct

it is impossible to tell with the information given
G is congruent with C
B is congruent with F
H is congruent with P

Answer 1

Given the congruence statement \( \triangle BGH \cong \triangle PCF \), we can infer that the corresponding parts of the triangles are congruent. The correct statements based on the congruence are:

1. \( BG \) is congruent to \( PC \)
2. \( GH \) is congruent to \( CF \)
3. \( BH \) is congruent to \( PF \)
4. \( \angle B \) is congruent to \( \angle P \)
5. \( \angle G \) is congruent to \( \angle C \)
6. \( \angle H \) is congruent to \( \angle F \)

From the options you provided:

- **G is congruent with C** - This is true, as \( \angle G \cong \angle C \).

- **B is congruent with F** - This is false; \( \angle B \) is congruent to \( \angle P \), not \( \angle F \).

- **H is congruent with P** - This is also false; \( \angle H \) is congruent to \( \angle F \), not \( \angle P \).

- **It is impossible to tell with the information given** - This is not true; we can conclude specific congruences based on the given information.

The correct statement is **G is congruent with C**.