Question

click the arrows to choose an answer from each menu. li choose... correct. each side length of abcd is choose... the corresponding side length of abcd. each angle measure of abcd is choose... the corresponding angle measure of abcd. therefore, abcd and abcd are choose...

Explanation:

To solve this, we analyze the transformation between quadrilaterals \( A'B'C'D' \) and \( ABCD \):

Step 1: Side Lengths

A translation (or rigid transformation) preserves side lengths. So each side length of \( A'B'C'D' \) is equal to the corresponding side length of \( ABCD \).

Step 2: Angle Measures

Rigid transformations (like translation) also preserve angle measures. Thus, each angle measure of \( A'B'C'D' \) is equal to the corresponding angle measure of \( ABCD \).

Step 3: Similarity/Congruence

Since all corresponding sides and angles are equal, \( A'B'C'D' \) and \( ABCD \) are congruent (and also similar, but congruence is more precise here as it implies equal sides/angles).

Final Answers (Filling the Menus):

• First “Choose”: (Assuming context about the transformation being a translation, which is a rigid motion)
• “Each side length of \( A'B'C'D' \) is”: \(\boldsymbol{\text{equal to}}\)
• “Each angle measure of \( A'B'C'D' \) is”: \(\boldsymbol{\text{equal to}}\)
• “Therefore, \( A'B'C'D' \) and \( ABCD \) are”: \(\boldsymbol{\text{congruent}}\) (or “similar and congruent,” but congruence is accurate for rigid transformations).

(Note: If the first “Choose” refers to the type of transformation, it is a translation (since \( A'B'C'D' \) is shifted left/right/up/down from \( ABCD \) without stretching or rotating).)

Answer:

To solve this, we analyze the transformation between quadrilaterals \( A'B'C'D' \) and \( ABCD \):

Step 1: Side Lengths

A translation (or rigid transformation) preserves side lengths. So each side length of \( A'B'C'D' \) is equal to the corresponding side length of \( ABCD \).

Step 2: Angle Measures

Rigid transformations (like translation) also preserve angle measures. Thus, each angle measure of \( A'B'C'D' \) is equal to the corresponding angle measure of \( ABCD \).

Step 3: Similarity/Congruence

Since all corresponding sides and angles are equal, \( A'B'C'D' \) and \( ABCD \) are congruent (and also similar, but congruence is more precise here as it implies equal sides/angles).

Final Answers (Filling the Menus):

• First “Choose”: (Assuming context about the transformation being a translation, which is a rigid motion)
• “Each side length of \( A'B'C'D' \) is”: \(\boldsymbol{\text{equal to}}\)
• “Each angle measure of \( A'B'C'D' \) is”: \(\boldsymbol{\text{equal to}}\)
• “Therefore, \( A'B'C'D' \) and \( ABCD \) are”: \(\boldsymbol{\text{congruent}}\) (or “similar and congruent,” but congruence is accurate for rigid transformations).

(Note: If the first “Choose” refers to the type of transformation, it is a translation (since \( A'B'C'D' \) is shifted left/right/up/down from \( ABCD \) without stretching or rotating).)