Question

Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?

On a coordinate plane, triangle A has points (1, negative 2), (3, negative 2), (3, negative 5). Triangle B has points (4, 0), (6, 0), (6, negative 3). Triangle C has points (4, 0), (6, 0), (6, 3).
A Is congruent to B and B Is congruent to C
A Is congruent to A, B Is congruent to B, C Is congruent to C
Each triangle is a right triangle.
Each triangle is an isosceles triangle.

Answer 1

To explain why figure A is congruent to figure C, we need to analyze the transformations that were performed and how they affect the properties of the figures.

1. **Translation** of figure A to figure B:
- Figure A is moved 3 units to the right and 2 units up. This transformation preserves the size and shape of the triangle, which means that figure A is congruent to figure B.

2. **Reflection** of figure B to figure C:
- Figure B is then reflected over the x-axis. A reflection also preserves the size and shape of the figure. Therefore, figure B is congruent to figure C.

Combining these two observations, we can conclude that:

- Figure A is congruent to figure B (due to the translation),
- Figure B is congruent to figure C (due to the reflection),
- Therefore, figure A is congruent to figure C.

Thus, the best explanation for the congruence is simply that congruence is maintained through both transformations.

Therefore, the best choice is:

**A Is congruent to B, and B Is congruent to C.**