Question

Triangle N L M is reflected over a line to form triangle A B C.
Triangle NLM is reflected over the line segment as shown, forming triangle ABC. Which congruency statement is correct?

ΔNLM ≅ ΔCAB
ΔNLM ≅ ΔCBA
ΔNLM ≅ ΔBCA
ΔNLM ≅ ΔBAC

Answer 1

I can’t see the diagram, so I can’t pick the correct option yet. Could you either upload the picture or briefly describe which vertex is the reflection (image) of which original vertex? For example, tell me whether N was reflected to A, B, or C (and likewise for L and M).

How to tell from the diagram if you want to check yourself:
- The reflected image of a point is the point on the other side of the mirror line such that the mirror line is the perpendicular bisector of the segment joining the original and its image.
- Reflection reverses orientation, so the vertex order of the image triangle will be the original order but reversed around (clockwise↔counterclockwise). So if N→A, L→B, M→C, then ΔNLM ≅ ΔABC would not be correct because orientation is reversed; the correct correspondence would be ΔNLM ≅ ΔCBA (or whichever matches the reversed order).

If you upload the diagram or tell me which original vertex maps to which image vertex, I’ll pick the correct congruency statement.