Question

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

Explanation:

Step1: Recall the property of reflection

Reflection is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, the reflected triangle \( \triangle ABC\) is congruent to the original triangle \( \triangle NLM\). Also, when writing congruency statements, the order of the vertices must correspond.

Step2: Match the vertices

In \( \triangle NLM\) and its reflection \( \triangle ABC\), vertex \(N\) corresponds to vertex \(C\), vertex \(L\) corresponds to vertex \(B\), and vertex \(M\) corresponds to vertex \(A\).

Answer:

\(\triangle NLM\cong\triangle CBA\)