Question

Which statement best explains whether △ABC is congruent to △DEF?

Responses

​△ABC​ is congruent to △DEF because △ABC can be mapped to △DEF by a translation 5 units down followed by a reflection across the x-axis.
​, triangle A B C, ​ , is congruent to , triangle D E F, because , triangle A B C, can be mapped to , triangle D E F, by a translation 5 units down followed by a reflection across the, x, -axis.

​△ABC is congruent to △DEF because △ABC can be mapped to △DEF by a reflection across the y-axis followed by a translation 5 units down.
​, triangle A B C, is congruent to , triangle D E F, because , triangle A B C, can be mapped to , triangle D E F, by a reflection across the , y, -axis followed by a translation 5 units down.

△ABC is not congruent to △DEF because there is no sequence of rigid motions that maps △ABC to △DEF.
triangle A B C, is not congruent to , triangle D E F, because there is no sequence of rigid motions that maps , triangle A B C, to , triangle D E F, .

​△ABC​ is congruent to △DEF because △ABC can be mapped to △DEF by a rotation of 90° counterclockwise about the origin followed by a reflection across the y-axis.
​, triangle A B C, ​ , is congruent to , triangle D E F, because , triangle A B C, can be mapped to , triangle D E F, by a rotation of 90° counterclockwise about the origin followed by a reflection across the, y, -axis.
Two triangles are graphed on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. In triangle A B C, the vertex labeled as A lies on begin ordered pair 3 comma 4 end ordered pair. The vertex labeled as B lies on begin ordered pair 3 comma 1 end ordered pair. The vertex labeled as C lies on begin ordered pair 1 comma 1 end ordered pair. In triangle D E F, the vertex labeled as D lies on begin ordered pair negative 3 comma negative 1 end ordered pair. The vertex labeled as E lies on begin ordered pair negative 3 comma negative 4 end ordered pair. The vertex labeled as F lies on begin ordered pair negative 1 comma negative 4 end ordered pair.

Answer 1

The statement that best explains whether △ABC is congruent to △DEF is (b)

Which statement best explains whether △ABC is congruent to △DEF?

From the question, we have the following parameters that can be used in our computation:

The triangles ABC and DEF

Reflecting ABC across the y-axis will negate the x-coordinates, which will place it directly above triangle DEF.

Counting down from A to D, B to E and C to F, we see that each is 5 units above the image; this means a translation 5 units down will finish mapping the pre-image to the image.

Since they are mapped on top of each other, they are congruent.

So, the true statement is (b)