Question

consider figures 1 through 4 on the coordinate plane. which two statements about these figures are true? all four figures are congruent because each figure can be mapped onto any other figure using a sequence of rigid transformations. figures 1 and 3 are not congruent because figure 1 cannot be mapped onto figure 3 using a sequence of rigid transformations. figures 1 and 2 are not congruent because figure 1 cannot be mapped onto figure 2 using a sequence of rigid transformations. figures 1 and 4 are not congruent because figure 1 cannot be mapped onto figure 4 using a sequence of rigid transformations. figures 2 and 4 are congruent because figure 2 can be mapped onto figure 4 using a sequence of rigid transformations.

Explanation:

1. Analyze "All four figures are congruent...": Rigid transformations (translation, rotation, reflection) preserve congruence. But visually, the figures have different sizes (e.g., Figure 4 looks larger than Figure 1), so they aren’t all congruent. Eliminate this.
2. Analyze "Figures 1 and 3 are not congruent...": Figure 1 and Figure 3: Check their shapes/sizes. Figure 1 is a small quadrilateral, Figure 3 is a larger quadrilateral. Since rigid transformations don’t change size, Figure 1 can’t map to Figure 3 (different size), so this statement is true.
3. Analyze "Figures 1 and 2 are not congruent...": Figure 1 (orange) and Figure 2 (pink): Visually, they appear to have the same shape and size (congruent). A sequence of rigid transformations (e.g., rotation, translation) could map one to the other. So this statement is false (they are congruent), eliminate.
4. Analyze "Figures 1 and 4 are not congruent...": Figure 1 (small) and Figure 4 (large green): Different sizes, so rigid transformations (which preserve size) can’t map Figure 1 to Figure 4. This statement is true.
5. Analyze "Figures 2 and 4 are congruent...": Figure 2 (pink, same size as Figure 1) and Figure 4 (large green): Different sizes, so they aren’t congruent. Eliminate.

So the true statements are "Figures 1 and 3 are not congruent because figure 1 cannot be mapped onto figure 3 using a sequence of rigid transformations" and "Figures 1 and 4 are not congruent because figure 1 cannot be mapped onto figure 4 using a sequence of rigid transformations".

Answer:

• Figures 1 and 3 are not congruent because figure 1 cannot be mapped onto figure 3 using a sequence of rigid transformations.
• Figures 1 and 4 are not congruent because figure 1 cannot be mapped onto figure 4 using a sequence of rigid transformations.