Question

△cde was translated down and right to form triangle △cde. which statements are true? check all that apply. □ de ≅ de □ ec ≅ ec □ ed ≅ dc □ cd ≅ de □ dc ≅ dc □ △cde ≅ △cde

Explanation:

Step1: Recall translation property

Translation is a rigid - motion. Rigid - motions preserve side - lengths and angle - measures. So, corresponding sides of the pre - image and the image are congruent, and the two triangles are congruent.

Step2: Identify corresponding sides

In $\triangle CDE$ and $\triangle C'D'E'$, $\overline{DE}$ corresponds to $\overline{D'E'}$, $\overline{EC}$ corresponds to $\overline{E'C'}$, $\overline{CD}$ corresponds to $\overline{C'D'}$, $\overline{D'C'}$ corresponds to $\overline{DC}$.

Step3: Analyze each statement

• $\overline{DE}\cong\overline{D'E'}$: True, as they are corresponding sides of translated triangles.
• $\overline{EC}\cong\overline{E'C'}$: True, as they are corresponding sides of translated triangles.
• $\overline{ED}\cong\overline{D'C'}$: False, they are not corresponding sides.
• $\overline{CD'}\cong\overline{D'E'}$: False, they are not corresponding sides.
• $\overline{D'C'}\cong\overline{DC}$: True, as they are corresponding sides.
• $\triangle CDE\cong\triangle C'D'E'$: True, since translation is a rigid - motion.

Answer:

$\overline{DE}\cong\overline{D'E'}$, $\overline{EC}\cong\overline{E'C'}$, $\overline{D'C'}\cong\overline{DC}$, $\triangle CDE\cong\triangle C'D'E'$