Question

triangle cde is translated down and to the right, forming triangle cde. which congruency statement is correct?

△dce ≅ △dec
△dce ≅ △dce
△edc ≅ △cde
△edc ≅ △ced

Explanation:

Step1: Recall the property of translation

Translation is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, \(\triangle CDE\) and \(\triangle C'D'E'\) are congruent.

Step2: Match the corresponding vertices

When \(\triangle CDE\) is translated to get \(\triangle C'D'E'\), vertex \(C\) corresponds to \(C'\), vertex \(D\) corresponds to \(D'\), and vertex \(E\) corresponds to \(E'\).

In the congruence statement, the order of the vertices must match the corresponding vertices.

For \(\triangle EDC\), \(E\) corresponds to \(E'\), \(D\) corresponds to \(D'\), \(C\) corresponds to \(C'\). So \(\triangle EDC\cong\triangle E'D'C'\) (not in the options).

For \(\triangle DCE\), \(D\) corresponds to \(D'\), \(C\) corresponds to \(C'\), \(E\) corresponds to \(E'\). So \(\triangle DCE\cong\triangle D'C'E'\)

Answer:

\(\triangle DCE\cong\triangle D'C'E'\) (the second option)