Triangle CDA is the image of triangle ABC after a 180º rotation around the midpoint of segment AC. Triangle ECB is the image of triangle ABC after a 180º rotation around the midpoint of segment BC. Triangle CDA is the image of triangle ABC after a 180º rotation around the midpoint of segment AC. Triangle ECB is the image of triangle ABC after a 180º rotation around the midpoint of segment BC. Explain why ABCD and ABEC are parallelograms.

Because parallelograms can be divided into two equal triangles of different orientations.

Step-by-step explanation:

Rotation is a process in which a given shape or point is turned about a reference point or line to produce the image of the initial shape, both having different orientations. It is one of the types of solid transformation.

Since,

ΔCAD = ΔABC but of different orientations, then ABCD is a parallelogram.

Also,

ΔABC = ΔECB, so that ABEC is a parallelogram.

So then:

ΔCAD = ΔABC = ΔECB

Therefore, ABCD and ABEC are parallelograms.