Question

Figure B' is a dilation of figure B. Which of the following statements about the dilation are true? Choose all the correct answers. A) Figure B' is smaller than figure B. B) Figure B' is larger than figure B. C) The shape of figure B' is the same as figure B. D) The size of figure B' is the same as figure B. E) The angles in figure B' are congruent to the angles in figure B.

Answer 1

The statements about the dilation that are true are that Figure B' is smaller than Figure B, the shape is the same, and the angles remain congruent. Figure B' cannot be both smaller and larger than Figure B at the same time, and their sizes are not identical due to the dilation.

Step-by-step explanation:

When a figure is a dilation of another, it means that the figure has been scaled up or down while maintaining its proportions. Considering the characteristics of a dilation:

• True: If Figure B' is a dilation of Figure B, and it has been mentioned that the image is smaller, then Figure B' is smaller than Figure B (Figure 16.28 (b)).
• False: Since Figure B' is smaller, it cannot be larger than Figure B at the same time.
• True: Dilation does not change the shape, therefore, the shape of figure B' is the same as figure B.
• False: Since Figure B' is smaller, the size of Figure B' is not the same as Figure B.
• True: Dilation maintains angle congruency, so the angles in figure B' are congruent to the angles in figure B.

Therefore, the correct statements about the dilation are that Figure B' is smaller than Figure B, the shape of Figure B' is the same as Figure B, and the angles in Figure B' are congruent to the angles in Figure B.