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).

Answer choices:

1. A Is congruent to B and B Is congruent to C
2. A Is congruent to A, B Is congruent to B, C Is congruent to C
3. Each triangle is a right triangle.
4. Each triangle is an isosceles triangle.

Answer 1

1. A Is congruent to B and B Is congruent to C

Explanation:

The congruence between figure A and C can be demonstrated by using the transitive property, which states

`(A \cong B ) \ and \ (B \cong C) \implies (A \cong C)`

As you can observe in the given choices, the one that can be used as transitive property is 1.

Additionally, the transformations described are rigid transformations, which means the figure won't change its shapo or size. That's why we can established those congruences.