Bella wants to use rigid transformations to show that △GHI≅△LKJ to illustrate the SSS triangle congruence criterion. Which of the following could she do first?

Question

Translate △GHI along a vector that takes point G to point L.
Translate triangle upper G upper H upper I along a vector that takes point upper G to point upper L .

Translate △GHI along a vector that takes point G to point J.
Translate triangle upper G upper H upper I along a vector that takes point upper G to point upper J .

Translate △GHI along a vector that takes point I to point K.
Translate triangle upper G upper H upper I along a vector that takes point upper I to point upper K .

Translate △GHI along a vector that takes point I to point L.

Answer 1

To show that triangles \(\triangle GHI \cong \triangle LKJ\) using rigid transformations, Bella needs to first align a corresponding vertex of triangle \(GHI\) with a vertex of triangle \(LKJ\) that will help establish the side lengths.

Given this context, she should first use the translation that takes a vertex from \(\triangle GHI\) to a corresponding vertex in \(\triangle LKJ\).

The most logical choice among the options provided would be:

Translate \(\triangle GHI\) along a vector that takes point \(G\) to point \(L\).

This step establishes a first point of correspondence between the triangles which will facilitate showing that the side lengths match up for the SSS congruence criterion. After translating point \(G\) to \(L\), further rigid transformations (like rotations or additional translations if needed) can be employed to align the other vertices appropriately.