Question

figure lmno maps to lmno by a 125° rotation about point t. which congruency statement is correct? ○ lmno ≅ lmno ○ lmno ≅ omnl ○ onml ≅ monl ○ onml ≅ omnl

Explanation:

Step1: Recall Rotation Congruence

A rotation is a rigid transformation, so the pre - image (LMNO) and the image (L'M'N'O') are congruent. Also, we need to check the order of the vertices to ensure the correspondence is correct.

Step2: Analyze Vertex Correspondence

• For option 1: Since LMNO is rotated to L'M'N'O', the vertex correspondence is L→L', M→M', N→N', O→O'. So \( LMNO\cong L'M'N'O' \) because rotation preserves congruence and the vertex order is correct.
• For option 2: The vertex order \( LMNO\cong O'M'N'L' \) does not follow the correct correspondence from the rotation. The rotation maps L to L', not to O', so this is incorrect.
• For option 3: The pre - image here is ONML (a re - ordering of LMNO) and the image \( M'O'N'L' \) does not have the correct vertex correspondence. The rotation should map O to O', N to N', M to M', L to L', so this is incorrect.
• For option 4: The pre - image is ONML and the image \( O'M'N'L' \) does not have the correct vertex correspondence. The rotation maps O to O', N to N', M to M', L to L', but the order of the pre - image (ONML) and the image \( O'M'N'L' \) does not match the rotation - induced correspondence.

Answer:

\( LMNO\cong L'M'N'O' \) (the first option: \( LMNO \cong L'M'N'O' \))