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, the translated triangle \(C'D'E'\) is congruent to the original triangle \(CDE\). The order of the vertices in the congruency statement should match the corresponding vertices.

Step2: Analyze each option

• For \(\triangle DCE\cong\triangle D'E'C'\): The order of vertices does not match the corresponding vertices after translation.
• For \(\triangle DCE\cong\triangle D'C'E'\): The order of vertices does not match the corresponding vertices after translation.
• For \(\triangle EDC\cong\triangle C'D'E'\):
• In \(\triangle EDC\), vertices are \(E\), \(D\), \(C\).
• In \(\triangle C'D'E'\), vertices are \(C'\), \(D'\), \(E'\). Since \(C\) corresponds to \(C'\), \(D\) corresponds to \(D'\), \(E\) corresponds to \(E'\), \(\triangle EDC\cong\triangle C'D'E'\) is correct as the order of vertices \(E - D - C\) in the first triangle corresponds to \(C' - D' - E'\) (because translation is a rigid - motion and the correspondence is based on the movement of each vertex. If we consider the movement of \(E\) to \(E'\), \(D\) to \(D'\), \(C\) to \(C'\), when writing the congruency statement, the order of vertices should follow the correspondence).
• For \(\triangle EDC\cong\triangle C'ED'\): The order of vertices does not match the corresponding vertices after translation.

Answer:

\(\triangle EDC\cong\triangle C'D'E'\) (the third option)