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 (likely a translation or scaling, but from the graph, it's a similarity transformation).

Step 1: Side Lengths

For similar figures, side lengths are proportional (or equal if congruent). Here, \( A'B'C'D' \) and \( ABCD \) have sides that are equal (since it's a translation or congruent transformation, or similar with scale factor 1). Wait, actually, checking coordinates:

• \( A'(2,0) \), \( A(4,2) \); \( B'(2,8) \), \( B(4,8) \); \( C'(7,5) \), \( C(8,6) \); \( D'(7,3) \), \( D(8,4) \). The horizontal/vertical distances: For \( A'B' \): vertical length \( 8 - 0 = 8 \); \( AB \): vertical length \( 8 - 2 = 6 \)? Wait, no, maybe it's a dilation? Wait, no, let's check slopes. Wait, actually, the key is: in similar figures, side lengths are proportional (if scale factor \( k \)), and angles are equal. If scale factor is 1, they are congruent (a type of similar figures with \( k=1 \)).

Step 2: Angle Measures

In similar (or congruent) figures, corresponding angles are equal (since it's a rigid transformation or similarity, angles preserve measure).

Step 3: Relationship

If side lengths are proportional (or equal, \( k=1 \)) and angles are equal, the figures are similar (congruent is a special case of similar with \( k=1 \)).

Filling the Blanks:

• Each side length of \( A'B'C'D' \) is equal to (or "proportional to" with \( k=1 \)) the corresponding side length of \( ABCD \).
• Each angle measure of \( A'B'C'D' \) is equal to the corresponding angle measure of \( ABCD \).
• Therefore, \( A'B'C'D' \) and \( ABCD \) are similar (or "congruent" if scale factor 1, but similar is more general).

(Assuming the first "Li Choose..." is a typo, focusing on the transformation questions.)

Final Answers (for the dropdowns):

• Side length: equal to (or proportional to, but likely "equal" if congruent)
• Angle measure: equal to
• Relationship: similar (or congruent)

(If forced to pick exact terms, typical answers: "equal to", "equal to", "similar" (or "congruent" if scale factor 1).)

Answer:

To solve this, we analyze the transformation (likely a translation or scaling, but from the graph, it's a similarity transformation).

Step 1: Side Lengths

For similar figures, side lengths are proportional (or equal if congruent). Here, \( A'B'C'D' \) and \( ABCD \) have sides that are equal (since it's a translation or congruent transformation, or similar with scale factor 1). Wait, actually, checking coordinates:

• \( A'(2,0) \), \( A(4,2) \); \( B'(2,8) \), \( B(4,8) \); \( C'(7,5) \), \( C(8,6) \); \( D'(7,3) \), \( D(8,4) \). The horizontal/vertical distances: For \( A'B' \): vertical length \( 8 - 0 = 8 \); \( AB \): vertical length \( 8 - 2 = 6 \)? Wait, no, maybe it's a dilation? Wait, no, let's check slopes. Wait, actually, the key is: in similar figures, side lengths are proportional (if scale factor \( k \)), and angles are equal. If scale factor is 1, they are congruent (a type of similar figures with \( k=1 \)).

Step 2: Angle Measures

In similar (or congruent) figures, corresponding angles are equal (since it's a rigid transformation or similarity, angles preserve measure).

Step 3: Relationship

If side lengths are proportional (or equal, \( k=1 \)) and angles are equal, the figures are similar (congruent is a special case of similar with \( k=1 \)).

Filling the Blanks:

• Each side length of \( A'B'C'D' \) is equal to (or "proportional to" with \( k=1 \)) the corresponding side length of \( ABCD \).
• Each angle measure of \( A'B'C'D' \) is equal to the corresponding angle measure of \( ABCD \).
• Therefore, \( A'B'C'D' \) and \( ABCD \) are similar (or "congruent" if scale factor 1, but similar is more general).

(Assuming the first "Li Choose..." is a typo, focusing on the transformation questions.)

Final Answers (for the dropdowns):

• Side length: equal to (or proportional to, but likely "equal" if congruent)
• Angle measure: equal to
• Relationship: similar (or congruent)

(If forced to pick exact terms, typical answers: "equal to", "equal to", "similar" (or "congruent" if scale factor 1).)