The figure shows three quadrilaterals on a coordinate grid:
A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. An image of a rectangle labeled A is shown on ordered pair 1, 1 and 3, 1 and 3, 2 and 1, 2. Another image of a rectangle labeled B is shown on ordered pair 2, 2 and 6, 2 and 6, 4 and 2, 4. Another image of a rectangle labeled C is shown on ordered pair negative 1, 1 and negative 1, 2, and negative 3 , 2 and negative 3, 1.
Which of the following statements is true about the three quadrilaterals? (5 points)
A. A and B are similar but not congruent.
B. A and C are similar but not congruent.
C. A and B are similar and also congruent.
D. B and C are similar and also congruent.
The answer can be found by examining the properties of the rectangles A, B, and C.
- For rectangles A and B, both have the same length of 2 units along the x-axis and 1 unit along the y-axis. The ratios of their side lengths are the same (2:1), so they are similar. However, their coordinates and dimensions are different, so they are not congruent.
- For rectangles A and C, they have different side lengths and dimensions, so they are not similar.
- For rectangles B and C, they have the same length of 4 units along the x-axis and 1 unit along the y-axis. The ratios of their side lengths are the same (4:1), so they are similar. Additionally, their coordinates and dimensions are also the same, so they are congruent.
Based on these observations, we can conclude that the statement "D. B and C are similar and also congruent" is true for the three quadrilaterals.