Question

determine if the two figures are congruent and explain your answer using transformations.

Explanation:

Step1: Translate the first figure

Translate the first figure (with vertices \(A\), \(B\), \(C\), \(D\)) 1 unit to the right and 4 units down.

Step2: Check for congruence

After translation, check if the corresponding sides and angles of the two figures are equal. Since translation is a rigid transformation (preserves shape and size), if after translation the two figures overlap exactly, they are congruent.

Answer:

The two figures are congruent. A translation (1 unit right and 4 units down) of the first - figure (with vertices \(A\), \(B\), \(C\), \(D\)) maps it onto the second - figure (with vertices \(E\), \(F\), \(G\), \(H\)). Rigid transformations (like translation) preserve the shape and size of a figure. So, the two figures have the same shape and size, which means they are congruent.