Since the image tells us that <F is congruent to <F in both triangles, an additional statement that would be enough to prove that[tex]\triangle EFI $ and $ \triangle GFH[/tex] are similar by the AA Similarity Postulate is: C. [tex]\mathbf{\angle E \cong \angle G}[/tex]
Recall:
Vertical angles have equal angle measure.
If we know that two angles in one triangle are congruent to two angles in another triangle, we can prove that the two triangles are similar by the Angle-Angle (AA) Similarity Postulate.
From the image given, we know that:
<F in [tex]\triangle EFI[/tex] is congruent to <F in [tex]\triangle GFH[/tex] because they are both vertically opposite to each other.
Therefore if we know that [tex]\angle E \cong \angle G[/tex], we can now prove that [tex]\triangle EFI $ and $ \triangle GFH[/tex] are similar because they have two corresponding angles that are congruent .
Therefore, since the image tells us that <F is congruent to <F in both triangles, an additional statement that would be enough to prove that[tex]\triangle EFI $ and $ \triangle GFH[/tex] are similar by the AA Similarity Postulate is: C. [tex]\mathbf{\angle E \cong \angle G}[/tex]
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