Question

identifying rigid transformations
the two triangles created by the diagonal of the parallelogram are congruent. recall that the opposite sides of a parallelogram are congruent.
which transformation(s) could map one triangle to the other?
reflection
translation
reflection and translation
rotation and translation

Explanation:

Step1: Analyze translation

Translation moves a figure without rotation or reflection. But in this case, just translation won't map one triangle to the other as their orientation relative to the diagonal (a line of symmetry - like a reflection aspect) is involved.

Step2: Analyze reflection

Reflection alone might seem possible, but since we are dealing with a parallelogram's diagonal - created triangles. A rotation (180 degrees around the center of the parallelogram) and then a translation (though in reality, for congruent triangles in a parallelogram divided by a diagonal, a 180 - degree rotation around the intersection point of the diagonals (which is the center of the parallelogram) is equivalent to a combination that can map one triangle to the other. In terms of rigid - transformation composition, rotation and translation (where the translation part is actually 'zero' in terms of non - rotational movement when considering the center - based rotation) conceptually can map one triangle to the other.

Answer:

rotation and translation