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 reflection

A reflection can flip one triangle over the diagonal (the line of symmetry in a sense for the two congruent triangles formed by the diagonal of a parallelogram) to map it onto the other triangle.

Step2: Analyze translation

A translation moves a figure without rotation or reflection. But just a simple translation (sliding) won't map one triangle (formed by the diagonal of a parallelogram) onto the other, because their orientation relative to each other is not just a shift - there is a 'flip' (which is addressed by reflection).

Step3: Analyze rotation and translation

Rotation changes the orientation of a figure around a point. The two triangles formed by the diagonal of a parallelogram are not related by a rotation (around a non - diagonal - related point) and then a translation. The key relationship is the reflection over the diagonal.

Answer:

reflection