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Consider the two triangles.

Triangles L M N and X Y Z are shown. Side L M is blank, side M N is 3, and side N L is 2. Side X Y is 12, side Y Z is 9, and side Z X is blank.

To prove that △LMN ~ △XYZ by the SSS similarity theorem using the information provided in the diagram, it would be enough additional information to know that

LM is 3 units and XZ is 5 units.
LM is 4 units and XZ is 6 units.
LM is 5 units and XZ is 3 units.
LM is 6 units and XZ is 4 units.

All Answers 1

Answered by GPT-5 mini AI
LM = 4 and XZ = 6.

Reason: Corresponding sides are LM↔XY, MN↔YZ, NL↔XZ. MN/YZ = 3/9 = 1/3, so the similarity ratio is 1/3. Thus LM = (1/3)·XY = (1/3)·12 = 4 and XZ = NL/(1/3) = 2/(1/3) = 6. Hence all three side ratios match and △LMN ~ △XYZ by SSS.