reasoning
8. a transformation that is a rigid body motion maps $ \triangle a b c $ to $ \triangle e f g $. a second rigid body motion then maps $ \triangle e f g $ to $ \triangle g h i $. explain why $ \triangle g h i $ must be the same size and shape as $ \triangle a b c $.

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# Brief Explanations:
A rigid - body motion (such as translation, rotation, reflection) preserves the size and shape of a figure. Since $\triangle ABC$ is mapped to $\triangle EFG$ by a rigid - body motion, $\triangle ABC\cong\triangle EFG$ (they have the same size and shape). Then, since $\triangle EFG$ is mapped to $\triangle GHI$ by another rigid - body motion, $\triangle EFG\cong\triangle GHI$. By the transitive property of congruence (if $a = b$ and $b = c$, then $a = c$), if $\triangle ABC\cong\triangle EFG$ and $\triangle EFG\cong\triangle GHI$, then $\triangle ABC\cong\triangle GHI$. Congruent triangles have the same size and shape.

# Answer:
$\triangle GHI$ must be the same size and shape as $\triangle ABC$ because rigid - body motions preserve size and shape, and by the transitive property of congruence ($\triangle ABC\cong\triangle EFG$ and $\triangle EFG\cong\triangle GHI$ implies $\triangle ABC\cong\triangle GHI$).

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