Question

a transformation was performed on figure 1 to create figure 2. figure 2 is rotated 45° clockwise to create figure 3 (not shown). which statement about the figures is true? a all 3 figures are similar. b all 3 figures are congruent. c only figure 2 and figure 3 are similar. d only figure 1 and figure 2 are congruent.

Explanation:

Step1: Recall the properties of rotation

Rotation is a transformation that preserves the shape and size of a figure. So, if Figure 1 is rotated to get Figure 2, they are congruent. Congruent figures are also similar (since the ratio of their corresponding sides is \(1:1\)). But we have no information about Figure 3.

Step2: Analyze each option

• Option A: We don't know about Figure 3's similarity to Figure 1 and 2. So, we can't say all 3 are similar.
• Option B: We don't know about Figure 3's congruence to Figure 1 and 2. So, we can't say all 3 are congruent.
• Option C: We have no information about Figure 3's similarity to Figure 2.
• Option D: Since rotation preserves shape and size, Figure 1 and Figure 2 are congruent.

Answer:

D. Only Figure 1 and Figure 2 are congruent.