Question

Triangle ABC maps to A′B′C′ as shown.

A triangle with vertices A at negative 3 comma 5, B at 3 comma 5, and C at 3 comma 1. A second triangle with vertices at A prime at negative 3 comma negative 3, B prime at 3 comma negative 3, and C prime at 3 comma negative 7.

Is triangle ABC congruent to triangle A′B′C′? Why, or why not?

Yes, because a reflection is a rigid transformation
No, because a reflection is not a rigid transformation
Yes, because a translation is a rigid transformation
No, because a translation is not a rigid transformation

Answer 1

Answer: Yes, triangle ABC is congruent to triangle A′B′C′, because a reflection is a rigid transformation. A rigid transformation is a transformation that preserves .the size and shape of a figure, meaning that the corresponding sides and angles of the figure are congruent after the transformation. A reflection is a transformation that flips a figure over a line of symmetry, creating a mirror image. In this case, triangle ABC is reflected over the x-axis to produce triangle A′B′C′. The two triangles have the same side lengths and angle measures, so they are congruent by the SSS (Side-Side-Side) criterion.