Which transformation verifies congruence by sliding one triangle over another?

The transformation that verifies congruence by sliding one triangle over another is called a "translation" or a "slide." In a translation, all points of a figure move the same distance and in the same direction, maintaining the same shape and size. Essentially, one triangle is slid (or shifted) horizontally and/or vertically to coincide with the corresponding vertices of the other triangle.

In a geometric context, congruence means that two figures are identical in shape and size. When you perform a translation on one triangle and superimpose it onto the other, the two triangles are congruent if their corresponding sides and angles match. The movement is purely translational, and no rotation or reflection is involved.

In mathematical notation, if triangle ABC is congruent to triangle DEF by a translation, it is often written as:

△���≅△���

△ABC≅△DEF

Translation is one of the basic rigid transformations, along with rotation and reflection, that preserves shape and size.