The SSS Congruence Theorem Quick Check

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The SSS Congruence Theorem Quick Check
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Use the image to answer the question.

Two congruent triangles with different orientations are side by side. Their corresponding congruent sides are marked.

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?

(1 point)
Responses

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

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 .
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GPT-4o mini · Answer

To demonstrate that triangle $ \triangle GHI \cong \triangle LJK $ using the SSS (Side-Side-Side) congruence criterion through rigid transformations, Bella must align corresponding points in the two triangles. Since she is aiming to show $ \triangle GHI $ is congruent to $ \triangle LJK $ and correspondences are crucial, she should first translate $ \triangle GHI $ so that one of its points matches one of the corresponding points in $ \triangle LJK $. The first logical step would involve taking a point from $ \triangle GHI $ and aligning it with the corresponding point in $ \triangle LJK $. The best option would usually be translating point $ G $ to point $ J $ since they are likely corresponding points in the congruent triangles. So, the first step Bella should take is: **Translate $ \triangle GHI $ along a vector that takes point $ G $ to point $ J $.** This will help in setting up the congruence based on the SSS criterion if all corresponding sides are marked as congruent.