Question

triangle cde is translated down and to the right, forming triangle cde. which congruency statement is correct? ○ δdce ≅ δdec ○ δdce ≅ δdce ○ δedc ≅ δcde ○ δedc ≅ δced

Explanation:

Step1: Recall the property of translation

Translation is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, the pre - image and the image are congruent. Also, the order of the vertices in the congruence statement should match the corresponding vertices.

Step2: Identify corresponding vertices

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

Answer:

\(\triangle EDC\cong\triangle E'D'C'\) (Since the order of vertices in congruence statement should follow the correspondence of vertices after translation. When we consider \(\triangle EDC\), \(E\to E'\), \(D\to D'\), \(C\to C'\))