Suppose \( \triangle I T H \approx A P G \). Which congruency statement is true? \( 0 \overline{I T} \simeq \overline{A G} \) \( 0 \overline{T H} \cong \overline{A P} \) \( 0 \overline{T H} \cong \overline{A G} \) \( 0 \overline{I H} \simeq \overline{A G} \)

Given that \( \triangle I T H \approx A P G \), this indicates that the two triangles are similar. In similar triangles, corresponding sides are proportional, but they are not necessarily congruent unless the triangles are also congruent. To determine the correct congruency statement, we need to identify the corresponding sides of the triangles based on their similarity. 1. The sides of triangle \( I T H \) correspond to the sides of triangle \( A P G \) as follows: - \( \overline{I T} \) corresponds to \( \overline{A P} \) - \( \overline{T H} \) corresponds to \( \overline{P G} \) - \( \overline{I H} \) corresponds to \( \overline{A G} \) Now, let's analyze the statements provided: 1. \( 0 \overline{I T} \simeq \overline{A G} \) - This is incorrect because \( \overline{I T} \) corresponds to \( \overline{A P} \), not \( \overline{A G} \). 2. \( 0 \overline{T H} \cong \overline{A P} \) - This is incorrect because \( \overline{T H} \) corresponds to \( \overline{P G} \), not \( \overline{A P} \). 3. \( 0 \overline{T H} \cong \overline{A G} \) - This is incorrect because \( \overline{T H} \) corresponds to \( \overline{P G} \), not \( \overline{A G} \). 4. \( 0 \overline{I H} \simeq \overline{A G} \) - This is correct because \( \overline{I H} \) corresponds to \( \overline{A G} \). Thus, the true congruency statement is: \[ 0 \overline{I H} \simeq \overline{A G} \]