Question

triangle ghi is rotated 90° clockwise and then reflected over the y - axis. which congruency statement is true? △ghi ≅ △ghi △ghi ≅ △ihg ∠g ≅ ∠h ≅ ∠i ∠g ≅ ∠h ≅ ∠i

Explanation:

Step1: Recall the properties of rotation and reflection

Rotation and reflection are rigid transformations. Rigid transformations preserve the shape and size of the figure. So, the pre - image and the image are congruent.

Step2: Analyze each option

• For $\triangle GHI\cong\triangle G''H''I''$: Since rotation (a rigid transformation) by $90^{\circ}$ clockwise and then reflection (another rigid transformation) over the $y$ - axis are applied. Rigid transformations result in congruent figures. So, $\triangle GHI$ and $\triangle G''H''I''$ are congruent.
• For $\triangle GHI\cong\triangle IHG$: This would be true if it was a different type of congruence (like by SSS, SAS etc. based on side - angle relations), but the problem is about transformation - based congruence. The order of vertices in the congruence statement matters in terms of correspondence. Here, the transformation is not a simple re - labeling of vertices in the way $\triangle GHI\cong\triangle IHG$ suggests (it's a transformation of the entire figure, not just a vertex re - arrangement for the same triangle).
• For $\angle G\cong\angle H\cong\angle I$: There is no information given that $\triangle GHI$ is equiangular. Just because of transformations, we can't assume this angle - equality (transformations preserve angles of the figure, but we don't know the original angle relations of $\triangle GHI$ from the transformation description).
• For $\angle G''\cong\angle H''\cong\angle I''$: Similar to the above, we don't know if the transformed triangle $\triangle G''H''I''$ is equiangular. Transformations preserve the angles of the original figure, but we have no data on the original angles of $\triangle GHI$ to conclude this.

Answer:

$\triangle GHI\cong\triangle G''H''I''$