Question

On the coordinate plane, ΔABC ≅ ΔDEF by SSS. ΔABC translates 2 units to the left and 3 units down. Do the triangles remain congruent? Explain why or why not.

Answer 1

Yes because you are simply translating the shape and moving it and not changing the shape.

Answer 2

Answer: Yes, they are congruent.

Explanation:

Given: On the coordinate plane, ΔABC ≅ ΔDEF by SSS...........(1)

ΔABC translates 2 units to the left and 3 units down.

Let ΔA'B'C' be the translated image of ΔABC.

• A translation is rigid transformation that maps every point of a figure by the same distance in a given direction.

Since, all the rigid transformations create congruent images.

Hence, ΔA'B'C'≅ΔABC.........................(2)

From (1) and (2), we have

A'B'C'≅ΔDEF [Transitive property of equality]

Therefore, the triangles remains congruent.